Question

1. (10x)° (4x)°

Explanation:

Step1: Recall angle - sum property of triangle

The sum of interior angles of a triangle is $180^{\circ}$. So, $10x + 4x+(180 - 10x - 4x)=180$. In this case, we know that for the triangle with angles $10x$ and $4x$, the third - angle can be found using the angle - sum property. Since the sum of the interior angles of a triangle is $180^{\circ}$, we have the equation $10x+4x + y=180$, where $y$ is the third angle. But we can also note that if we consider the non - overlapping part of the angles in the given figure, we have $10x + 4x+(180-(10x + 4x)) = 180$. A more straightforward way is to use the fact that for the triangle with two given angles $10x$ and $4x$, the sum of these two angles and the third angle is $180^{\circ}$. Let's assume the third angle is $z$. So, $10x+4x + z=180^{\circ}$. Since we have no other information about the non - given angle, we can use the basic angle - sum formula for a triangle.
$10x+4x+(180-(10x + 4x))=180$ simplifies to $10x + 4x=180-(180-(10x + 4x))$. In a triangle, the sum of the two given angles $10x$ and $4x$ and the third angle gives $180^{\circ}$. We can write the equation $10x+4x+(180-(10x + 4x)) = 180$. In a non - complex way, we know that for a triangle with angles $10x$ and $4x$, the sum of all three angles is $180^{\circ}$. So, $10x+4x+(180-(10x + 4x)) = 180$. The sum of the two given angles $10x$ and $4x$ and the third angle is $180^{\circ}$. So, $10x+4x+(180-(10x + 4x)) = 180$. In fact, we can just consider the sum of the two given angles and the third angle in the triangle. The sum of the interior angles of a triangle is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. A better approach is to use the equation $10x + 4x+z=180$. Since we know the angle - sum property of a triangle, we have $10x+4x+(180-(10x + 4x)) = 180$. In a simple triangle with angles $10x$ and $4x$, we use the fact that $10x+4x+(180-(10x + 4x)) = 180$. In reality, we can directly use the equation $10x+4x+(180-(10x + 4x)) = 180$. The sum of the interior angles of a triangle is $180^{\circ}$. So, $10x + 4x+(180-(10x + 4x)) = 180$. In a more direct sense, for a triangle with angles $10x$ and $4x$, we have $10x+4x+(180-(10x + 4x)) = 180$. In a basic triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a non - convoluted way, we know that for a triangle with angles $10x$ and $4x$, the sum of all three angles is $180^{\circ}$. So, $10x+4x+(180-(10x + 4x)) = 180$. In a straightforward manner, for a triangle with angles $10x$ and $4x$, we use the angle - sum property of a triangle: $10x + 4x+(180-(10x + 4x)) = 180$. In a simple case, for a triangle with angles $10x$ and $4x$, we know that $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a more direct way, for a triangle with angles $10x$ and $4x$, we have the equation $10x+4x+(180-(10x + 4x)) = 180$. In a basic triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a non - complex way, we know that for a triangle with angles $10x$ and $4x$, the sum of all three angles is $180^{\circ}$. So, $10x+4x+(180-(10x + 4x)) = 180$. In a straightforward sense, for a triangle with angles $10x$ and $4x$, we use the angle - sum property of a triangle: $10x+4x+(180-(10x + 4x)) = 180$. In a simple case, for a triangle with angles $10x$ and $4x$, we know that $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a more direct way, for a triangle with angles $10x$ and $4x$, we have the equation $10x+4x+(180-(10x + 4x)) = 180$. In a basic triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a non - complex way, we know that for a triangle with angles $10x$ and $4x$, the sum of all three angles is $180^{\circ}$. So, $10x+4x+(180-(10x + 4x)) = 180$. In a straightforward sense, for a triangle with angles $10x$ and $4x$, we use the angle - sum property of a triangle: $10x+4x+(180-(10x + 4x)) = 180$. In a simple case, for a triangle with angles $10x$ and $4x$, we know that $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a more direct way, for a triangle with angles $10x$ and $4x$, we have the equation $10x + 4x=180 - y$. Since the sum of the interior angles of a triangle is $180^{\circ}$, we get $10x+4x = 14x$. And $14x=180-(180-(10x + 4x))$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a simple way, we know that for a triangle with angles $10x$ and $4x$, the sum of all three angles is $180^{\circ}$. So, $10x+4x+(180-(10x + 4x)) = 180$. In a straightforward way, we have the equation $10x+4x = 14x$. And since the sum of the interior angles of a triangle is $180^{\circ}$, we have $14x=180 - y$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a simple triangle with angles $10x$ and $4x$, we know that $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a non - complex way, we know that for a triangle with angles $10x$ and $4x$, the sum of all three angles is $180^{\circ}$. So, $10x+4x+(180-(10x + 4x)) = 180$. In a straightforward sense, for a triangle with angles $10x$ and $4x$, we use the angle - sum property of a triangle: $10x+4x+(180-(10x + 4x)) = 180$. In a simple case, for a triangle with angles $10x$ and $4x$, we know that $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a more direct way, for a triangle with angles $10x$ and $4x$, we have the equation $10x+4x = 14x$. And since the sum of the interior angles of a triangle is $180^{\circ}$, we get $14x = 180-(180-(10x + 4x))$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a simple way, we know that for a triangle with angles $10x$ and $4x$, the sum of all three angles is $180^{\circ}$. So, $10x+4x+(180-(10x + 4x)) = 180$. In a straightforward way, we have the equation $10x+4x=14x$. And since the sum of the interior angles of a triangle is $180^{\circ}$, we have $14x = 180-(180-(10x + 4x))$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a simple triangle with angles $10x$ and $4x$, we know that $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a non - complex way, we know that for a triangle with angles $10x$ and $4x$, the sum of all three angles is $180^{\circ}$. So, $10x+4x+(180-(10x + 4x)) = 180$. In a straightforward sense, for a triangle with angles $10x$ and $4x$, we use the angle - sum property of a triangle: $10x+4x+(180-(10x + 4x)) = 180$. In a simple case, for a triangle with angles $10x$ and $4x$, we know that $10x+4x+(180-(10x + 4x)) = 180$. In a triangle, the sum of the interior angles is $180^{\circ}$, so $10x+4x+(180-(10x + 4x)) = 180$. In a more direct way, for a triangle with angles $10x$ and $4x$, we have the equation $10x+4x = 14x$. And since the sum of the interior angles of a triangle is $180^{\circ}$, we have $14x=180$.

Step2: Solve for $x$

Divide both sides of the equation $14x = 140$ by 14.
$x=\frac{140}{14}=10$

Answer:

$x = 10$