Question

1. in the given figure, e is the intersection of \\( \overline { a b } \\) and \\( \overline { c d } \\) :

what is the measure of \\( \angle d a e \\) ?
\\( 57 ^ { \circ } \\)
\\( 42 ^ { \circ } \\)
\\( 85 ^ { \circ } \\)
\\( 43 ^ { \circ } \\)

Explanation:

Step1: Find the measure of ∠AED

Since ∠BEC and ∠AED are vertical angles, they are equal. So, ∠AED = 95°.

Step2: Use the triangle angle - sum property

In triangle ADE, the sum of angles is 180°. Let ∠DAE = x. Then \(x + 43^{\circ}+95^{\circ}=180^{\circ}\).

Step3: Solve for x

\(x=180^{\circ}-(43^{\circ} + 95^{\circ})\)
\(x = 180^{\circ}-138^{\circ}\)
\(x = 42^{\circ}\)

Answer:

\(42^{\circ}\)