Question

unit 4 test
find m∠y.
(6x - 23)°
(4x + 9)°

Explanation:

Step1: Use isosceles - triangle property

Since the two sides of the triangle are congruent (marked with single - hash marks), the base - angles are congruent. So, $\angle X=\angle Z$.
$6x - 23=4x + 9$

Step2: Solve for $x$

Subtract $4x$ from both sides: $6x-4x - 23=4x-4x + 9$, which simplifies to $2x-23 = 9$.
Add 23 to both sides: $2x-23 + 23=9 + 23$, so $2x=32$.
Divide both sides by 2: $x = 16$.

Step3: Find the measure of $\angle X$ or $\angle Z$

Substitute $x = 16$ into the expression for $\angle Z$: $\angle Z=4x + 9=4\times16+9=64 + 9=73^{\circ}$.

Step4: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle Y=y$. Then $y+\angle X+\angle Z=180^{\circ}$. Since $\angle X=\angle Z = 73^{\circ}$, we have $y+73^{\circ}+73^{\circ}=180^{\circ}$.
$y=180-(73 + 73)=180 - 146=34^{\circ}$.

Answer:

$34^{\circ}$