Question

find the measure of the missing angles. answer attempt 1 out of 2 d = ° e = ° f = ° submit answer

Explanation:

Step1: Use linear - pair property for \(d\)

A linear pair of angles sums to \(180^{\circ}\). Since \(d\) and \(131^{\circ}\) form a linear pair, \(d = 180 - 131\).
\[d=49^{\circ}\]

Step2: Use angle - addition property for \(e\)

We know that \(d + 27^{\circ}+e=180^{\circ}\) (a straight - line angle). Substitute \(d = 49^{\circ}\) into the equation: \(49+27 + e=180\), so \(e=180-(49 + 27)\).
\[e = 104^{\circ}\]

Step3: Use vertical - angle property for \(f\)

\(f\) and the angle composed of \(27^{\circ}\) and \(d\) are vertical angles. The angle composed of \(27^{\circ}\) and \(d\) is \(27 + 49=76^{\circ}\), and vertical angles are equal, so \(f = 76^{\circ}\).

Answer:

\(d = 49^{\circ}\), \(e = 104^{\circ}\), \(f = 76^{\circ}\)