Question

find the measure of each numbered angle.

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle1\) and \(\angle2\) be the two unknown angles. We know that \(\angle1+\angle2 + 146^{\circ}=180^{\circ}\).

Step2: Simplify the equation

Subtract \(146^{\circ}\) from both sides of the equation: \(\angle1+\angle2=180^{\circ}- 146^{\circ}\). So, \(\angle1+\angle2 = 34^{\circ}\).

Step3: Assume \(\angle1=\angle2\) (isosceles triangle assumption, as no other information about side - angle relationships is given except the single non - base angle)

If \(\angle1=\angle2\), then \(\angle1=\angle2=\frac{34^{\circ}}{2}\)

Answer:

\(\angle1 = 17^{\circ}\), \(\angle2=17^{\circ}\)