Question

find the measure of the missing angles. 105° 32° answer attempt 1 out of 2 d = \boxed{}^circ e = \boxed{}^circ f = \boxed{}^circ

Explanation:

Step1: Find \( d \)

Angles on a straight line sum to \( 180^\circ \). So \( d + 105^\circ = 180^\circ \), then \( d = 180^\circ - 105^\circ = 75^\circ \).

Step2: Find \( e \)

Vertical angles are equal. The angle opposite to \( e \) is \( 32^\circ \), so \( e = 32^\circ \).

Step3: Find \( f \)

Angles around a point sum to \( 180^\circ \) (for the straight line related to \( d \), \( e \), and \( f \)). So \( d + e + f = 180^\circ \). Substitute \( d = 75^\circ \) and \( e = 32^\circ \), we get \( 75^\circ + 32^\circ + f = 180^\circ \). Then \( f = 180^\circ - 75^\circ - 32^\circ = 73^\circ \).

Answer:

\( d = 75^\circ \), \( e = 32^\circ \), \( f = 73^\circ \)