Question

1. in the diagram shown, points a, b, and c all lie on a straight line. it is known that m∠ebc = 128° and m∠dbc = 35°. answer the following questions: (a) find the measures of ∠ebd and ∠abe. (b) is $overline{be}perpoverline{bd}$? justify your yes/no answer.

Explanation:

Step1: Find measure of ∠EBD

Since ∠EBC = ∠EBD+∠DBC, then ∠EBD=∠EBC - ∠DBC.
∠EBD = 128° - 35°=93°

Step2: Find measure of ∠ABE

Since points A, B, C are on a straight - line, ∠ABC = 180°. So ∠ABE=180° - ∠EBC.
∠ABE = 180° - 128° = 52°

Step3: Determine if BE⊥BD

Two lines are perpendicular if the angle between them is 90°. Since ∠EBD = 93°≠90°, BE is not perpendicular to BD.

Answer:

(a) m∠EBD = 93°, m∠ABE = 52°
(b) No, because m∠EBD = 93°≠90°.