Question

1. if ∠def is a right - angle and m∠dey=\frac{1}{2}x + 34, then what is the value of x?
2. if ∠tmi = 5x+2 and x = 20, then classify ∠tmi as acute, obtuse, right, or straight. explain your choice.
3. in the diagram shown, points a, b, and c are collinear and be⊥ac.

(a) state one pair of complementary angles.
(b) state two pairs of supplementary angles.

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

Step2: Find measure of ∠ABE

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

Step3: Check 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) ∠EBD = 93°, ∠ABE = 52°
(b) No, because the measure of ∠EBD is 93° which is not 90°.