Question

find the measure of each numbered angle: 49° 71° 53°

Explanation:

Step1: Find angle 1

Use the triangle angle - sum theorem (\(180^{\circ}\) in a triangle).
\(\angle1=180^{\circ}-49^{\circ}-71^{\circ}\)
\(\angle1 = 60^{\circ}\)

Step2: Find angle 2

Vertical angles are equal. Since \(\angle1\) and \(\angle2\) are vertical angles.
\(\angle2=\angle1\)
\(\angle2 = 60^{\circ}\)

Step3: Find angle 3

\(\angle1+\angle3 = 180^{\circ}\) (linear pair).
\(\angle3=180^{\circ}-\angle1\)
\(\angle3=180^{\circ}-60^{\circ}\)
\(\angle3 = 120^{\circ}\)

Step4: Find angle 4

Use the right - triangle angle - sum theorem (\(90^{\circ}+53^{\circ}+\angle4 = 180^{\circ}\)).
\(\angle4=180^{\circ}-90^{\circ}-53^{\circ}\)
\(\angle4 = 37^{\circ}\)

Step5: Find angle 6

Use the right - triangle angle - sum theorem (\(90^{\circ}+\angle4+\angle6 = 180^{\circ}\)).
\(\angle6=180^{\circ}-90^{\circ}-\angle4\)
\(\angle6=180^{\circ}-90^{\circ}-37^{\circ}\)
\(\angle6 = 53^{\circ}\)

Step6: Find angle 5

Use the triangle angle - sum theorem (\(\angle5+\angle1+\angle6 = 180^{\circ}\)).
\(\angle5=180^{\circ}-\angle1-\angle6\)
\(\angle5=180^{\circ}-60^{\circ}-53^{\circ}\)
\(\angle5 = 67^{\circ}\)

Answer:

\(\angle1 = 60^{\circ}\), \(\angle2 = 60^{\circ}\), \(\angle3 = 120^{\circ}\), \(\angle4 = 37^{\circ}\), \(\angle5 = 67^{\circ}\), \(\angle6 = 53^{\circ}\)