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 \(25x + 3=(10x + 2)+76\).

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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 \(66=(3x + 11)+(3x + 1)\).

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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. \(38^{\circ}\)