Question

(d) problem 20: (first taught in lesson 17)
if z = 2x and y = 3x, find x.

Explanation:

Step1: Use angle - sum property

The exterior angle $y$ of the triangle is equal to the sum of the two non - adjacent interior angles. So $y=x + z$.

Step2: Substitute given values

Given $z = 2x$ and $y=3x$. Substitute into $y=x + z$, we get $3x=x + 2x$. Also, in terms of angle relationships, since $y$ is an exterior angle and $x,z$ are non - adjacent interior angles, and $y = 3x,z = 2x$, and we know that for a triangle, the sum of interior angles and exterior - interior angle relationships hold. Another way is to use the fact that the sum of angles on a straight line is $180^{\circ}$. So $y+z = 180^{\circ}$. Substitute $y = 3x$ and $z = 2x$ into $y + z=180^{\circ}$, we have $3x+2x=180^{\circ}$.

Step3: Solve for $x$

Combining like terms in $3x + 2x=180^{\circ}$, we get $5x=180^{\circ}$. Then $x=\frac{180^{\circ}}{5}=36^{\circ}$. So $x = 36$.

Answer:

$36$