Question

for each of the following, find the indicated angle measures. be sure that you record your answer in the correct answer blank. figures are not drawn to scale. 19. 20. 21. two angles of a triangle have measures of

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. In the first figure, angle \(c\) and the \(47^{\circ}\) angle are vertical angles, so \(c = 47^{\circ}\).

Step2: Find angle \(a\) in the first triangle

In the upper - triangle of the first figure, using the angle - sum property of a triangle (\(a + 59^{\circ}+47^{\circ}=180^{\circ}\)). Then \(a=180^{\circ}-(59^{\circ} + 47^{\circ})=74^{\circ}\).

Step3: Find angle \(b\) in the first figure

In the lower - triangle of the first figure, using the angle - sum property of a triangle (\(b + 64^{\circ}+47^{\circ}=180^{\circ}\)). Then \(b = 180^{\circ}-(64^{\circ}+47^{\circ}) = 69^{\circ}\).

Step4: Find angle \(d\) in the second figure

In the second figure, angle \(d\) and the \(39^{\circ}\) angle are vertical angles, so \(d = 39^{\circ}\).

Step5: Find angle \(e\) in the second figure

In the triangle with angles \(45^{\circ}\), \(d = 39^{\circ}\), and \(e\), using the angle - sum property of a triangle (\(e=180^{\circ}-(45^{\circ}+39^{\circ}) = 96^{\circ}\)).

Step6: Find angle \(f\) in the second figure

Angle \(f\) and the \(43^{\circ}\) angle are vertical angles, so \(f = 43^{\circ}\).

Answer:

1. \(a = 74\), \(b = 69\), \(c = 47\)
2. \(d = 39\), \(e = 96\), \(f = 43\)