Question

1. find x and m∠y.

(6x - 23)°
(4x + 9)°
x =
m∠y =

Explanation:

Step1: Use isosceles - triangle property

Since the triangle has two equal - sides (marked with single hash marks), the angles opposite those sides are equal. So, \(6x - 23=4x + 9\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(6x-4x - 23=4x-4x + 9\), which simplifies to \(2x-23 = 9\). Then add 23 to both sides: \(2x-23 + 23=9 + 23\), getting \(2x=32\). Divide both sides by 2: \(x = 16\).

Step3: Find the measure of \(\angle Y\)

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle X=6x - 23\) and \(\angle Z = 4x + 9\). Substitute \(x = 16\) into \(\angle X\) and \(\angle Z\): \(\angle X=6\times16-23=96 - 23 = 73^{\circ}\), \(\angle Z=4\times16 + 9=64 + 9 = 73^{\circ}\). Then \(m\angle Y=180-(73 + 73)=34^{\circ}\).

Answer:

\(x = 16\)
\(m\angle Y = 34^{\circ}\)