Question

problem 16: (first taught in lesson 30) find x and y.

Explanation:

Step1: Use angle - sum property of a straight - line

The angles on a straight - line sum to $180^{\circ}$. So, $3x+105 + x=180$.
Combining like terms, we get $4x+105 = 180$.
Subtract 105 from both sides: $4x=180 - 105=75$.
Divide both sides by 4: $x = 15$.

Step2: Use angle - sum property of a triangle

In the right - hand triangle, the sum of interior angles of a triangle is $180^{\circ}$.
We know one angle is $x = 15^{\circ}$ and another is $105^{\circ}$. Let the third angle be $2y^{\circ}$.
So, $15+105 + 2y=180$.
Combining like terms: $120+2y = 180$.
Subtract 120 from both sides: $2y=180 - 120 = 60$.
Divide both sides by 2: $y = 30$.

Answer:

$x = 15$, $y = 30$