Question

find the value of a and c.

a. \\(a = 3, c = 13.5\\)
b. \\(a = 2.4, c = 10.8\\)
c. \\(a = 3.2, c = 14.4\\)
d. \\(a = 2, c = 9\\)

Explanation:

Identify angle relationships

The diagram shows two parallel lines cut by a transversal. The interior angles on the same side of the transversal, \((5a + 98)^\circ\) and \((36a)^\circ\), are consecutive interior angles.

Solve for a

Using the Consecutive Interior Angles Theorem

$$
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Set up equation for c

Using the Linear Pair Postulate

$$ (8c) + (5a + 98) = 180 $$

Solve for c

Using the Linear Equations knowledge point

$$
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$$

Answer:

• (A) \(a = 3, c = 13.5\)
• (B) \(a = 2.4, c = 10.8\)
• (C) \(a = 3.2, c = 14.4\)
• (D) \(a = 2, c = 9\) (Correct answer)