Question

vertical/adjacent/complementary angles l2
question
video examples
find the measure of the missing angles.
answer
attempt 2 out of 3
d =

e =

f =

Explanation:

Step1: Find \(d\)

Vertical angles are equal. The angle vertical to \(77^{\circ}\) is \(d + 31^{\circ}\). So \(d+31^{\circ}=77^{\circ}\).
Subtract \(31^{\circ}\) from both sides: \(d = 77^{\circ}-31^{\circ}=46^{\circ}\).

Step2: Find \(e\)

Vertical angles are equal. The angle vertical to \(31^{\circ}\) is \(e\). So \(e = 31^{\circ}\).

Step3: Find \(f\)

The sum of angles around a point is \(360^{\circ}\). We know three angles: \(77^{\circ}\), \(31^{\circ}\), and \(d = 46^{\circ}\), \(e = 31^{\circ}\).
\(f=360^{\circ}-(77^{\circ}+31^{\circ}+46^{\circ}+31^{\circ})\)
First, calculate the sum of the known angles: \(77 + 31+46 + 31=185^{\circ}\)
Then \(f = 360^{\circ}-185^{\circ}=175^{\circ}\)

Answer:

\(d = 46^{\circ}\), \(e = 31^{\circ}\), \(f = 175^{\circ}\)