Question

5 8.2.1 practice 5
in the picture, lines ac and df are parallel. find the measures of the following angles.
type the answers in the boxes below. be sure to include the degree symbol in your answer.
a. ∠abe=
b. ∠feh=
c. ∠cbe=

Explanation:

Step1: Find \(\angle ABE\)

Use the linear - pair relationship. \(\angle ABE + 108^{\circ}=180^{\circ}\). So \(\angle ABE = 180^{\circ}-108^{\circ}=72^{\circ}\).

Step2: Find \(\angle FEH\)

Since \(AC\parallel DF\), \(\angle FEH\) and \(\angle GBC\) (where \(\angle GBC = 108^{\circ}\)) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So \(\angle FEH = 108^{\circ}\).

Step3: Find \(\angle CBE\)

\(\angle CBE\) and \(\angle GBC\) are vertical angles. Vertical angles are equal. So \(\angle CBE = 108^{\circ}\).

Answer:

a. \(72^{\circ}\)
b. \(108^{\circ}\)
c. \(108^{\circ}\)