Question

1. what is the value of a?

(there is a geometric figure with points, segments labeled 70, 70, 3a, a + 60, and a right angle or some angle marking. the question is to find the value of a.)

Explanation:

Step1: Use the property of similar triangles

Since the two triangles are similar (by the AA similarity criterion as the vertical angles are equal), the ratios of corresponding sides are equal. So, \(\frac{10}{10 + 10}=\frac{8}{a + 8}\).

Step2: Simplify the left - hand side ratio

\(\frac{10}{20}=\frac{1}{2}\). So the equation becomes \(\frac{1}{2}=\frac{8}{a + 8}\).

Step3: Cross - multiply

Cross - multiplying gives \(a + 8=2\times8\).

Step4: Solve for \(a\)

\(a+8 = 16\), then \(a=16 - 8\).

Answer:

\(a = 8\)