Question

if these two figures are similar, what is the measure of the missing angle?

Explanation:

Step1: Recall angle - property of similar figures

Similar figures have equal corresponding angles.

Step2: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let the angles of the first triangle be \(42^{\circ}\), \(58^{\circ}\), and \(x\). Then \(42 + 58+x=180\).

Step3: Calculate the third - angle of the first triangle

First, add the given angles: \(42 + 58=100\). Then \(x = 180-100=80^{\circ}\).

Step4: Determine the missing angle of the second triangle

Since the two triangles are similar, the missing angle of the second triangle is equal to the third - angle of the first triangle, which is \(80^{\circ}\).

Answer:

\(80^{\circ}\)