Question

find the measure of each numbered angle.
m∠1 = , m∠2 =
(there is a triangle image with angle 1, angle 2, and a 146° angle at the top)

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). Let \(m\angle1 = x\) and \(m\angle2 = y\). The given angle is \(146^\circ\), so \(x + y+ 146^\circ=180^\circ\).

Step2: Identify isosceles triangle

The triangle is isosceles (two equal sides, so \(\angle1=\angle2\)), so \(x = y\). Substitute into the sum: \(2x + 146^\circ=180^\circ\).

Step3: Solve for x

Subtract \(146^\circ\) from both sides: \(2x=180^\circ - 146^\circ = 34^\circ\). Then divide by 2: \(x=\frac{34^\circ}{2}=17^\circ\). So \(m\angle1 = 17^\circ\) and \(m\angle2 = 17^\circ\).

Answer:

\(m\angle1 = 17^\circ\), \(m\angle2 = 17^\circ\)