Question

problem 6 determine the measure of the missing angle

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Let the missing angle be \(x\)

We know two angles: 20° and 72°, and a right - angle (90°). So \(x+20^{\circ}+72^{\circ}+90^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

First, add the known non - missing angles: \(20^{\circ}+72^{\circ}+90^{\circ}=182^{\circ}\), which is incorrect. Since it's a triangle, we should consider the non - right angle case. Let the angles of the triangle be \(A = 20^{\circ}\), \(B=72^{\circ}\), and the missing angle \(C\). Then \(A + B+C=180^{\circ}\). So \(C=180^{\circ}-(20^{\circ}+72^{\circ})\).
\[C = 180^{\circ}-92^{\circ}=88^{\circ}\]

Answer:

88°