Question

find the measure of angle 2. 118° 2

Explanation:

Step1: Find the adjacent angle of \(118^{\circ}\)

The adjacent angle of \(118^{\circ}\) is \(180^{\circ}- 118^{\circ}=62^{\circ}\) (supplementary angles).

Step2: Use the property of isosceles triangle

Since the two sides are equal, the base - angles of the isosceles triangle are equal. Let the base - angle be \(x\). Then \(x + x+62^{\circ}=180^{\circ}\) (sum of angles in a triangle). So \(2x=180^{\circ}-62^{\circ}=118^{\circ}\), \(x = 59^{\circ}\).

Step3: Use the right - angle property

We know that the right - angle is \(90^{\circ}\). Let \(\angle2\) be \(y\). Then \(y+59^{\circ}=90^{\circ}\) (because the two non - right angles in the right - angled part of the figure). So \(y=90^{\circ}-59^{\circ}=31^{\circ}\)

Answer:

\(31^{\circ}\)