Question

find the measure of the angle indicated. 15) find m∠zqr. 16) find m∠h.

Explanation:

Step1: Use exterior - angle property for first triangle

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. For \(\triangle SQR\), we have \(25x + 3=(10x + 2)+76\).
\[

$$\begin{align*} 25x+3&=10x + 2+76\\ 25x+3&=10x+78\\ 25x-10x&=78 - 3\\ 15x&=75\\ x& = 5 \end{align*}$$

\]

Step2: Find \(m\angle ZQR\)

Substitute \(x = 5\) into the expression for the exterior angle. \(m\angle ZQR=25x+3\).
\[m\angle ZQR=25\times5 + 3=125+3=128^{\circ}\]

Step3: Use exterior - angle property for second triangle

For \(\triangle HFG\), the exterior angle at \(F\) is \(66^{\circ}\), and we have \(66=(3x + 11)+(3x + 1)\).
\[

$$\begin{align*} 66&=3x+11 + 3x+1\\ 66&=6x+12\\ 6x&=66 - 12\\ 6x&=54\\ x&=9 \end{align*}$$

\]

Step4: Find \(m\angle H\)

Substitute \(x = 9\) into the expression for \(\angle H\), \(m\angle H=3x + 11\).
\[m\angle H=3\times9+11=27 + 11=38^{\circ}\]

Answer:

1. B. \(128^{\circ}\)
2. B. \(38^{\circ}\)