Question

Find the measure of each angle indicated

Answer 1

Explanation:

Angle Q = 74. Supplmentary to 106

Angle S = 72. 3rd Angle of Triangle. 180-34-74 =72.

Answer 2

72°

Explanation:

According to the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

Therefore, for the given triangle:

`m \angle R + m \angle S = m \angle RQG`

To find the measure of angle S, substitute the given values of angle R and the exterior angle RQG into the equation, and solve for m∠S:

`\begin{aligned} m \angle R + m \angle S &= m \angle RQG\\34^(\circ)+m \angle S &=106^(\circ)\\34^(\circ)+m \angle S-34^(\circ) &=106^(\circ)-34^(\circ)\\m \angle S &=72^(\circ)\end{aligned}`

Therefore, the measure of angle S is 72°.