Question

What’s the answer for the second rectangle on the bottom?

ANGLES - OW

Answer 1

1) 23°

2) 55°

Explanation:

Q1)

GIVEN :-

• ∠ADB = 64°
• ∠BEC = 49°

TO FIND :-

• ∠EBD or ∠a

PROCEDURE :-

ABCD is a rectangle. In a rectangle , all the angles measure 90°. So,

∠ADC = 90°

⇒ ∠ADB + ∠BDE = 90°

⇒ ∠BDE = 90 - 64 = 26°

In a triangle , measure of an exterior angle of a triangle is the sum of the two opposite interior angles. So in ΔEBD ,

∠EBD + ∠EDB = ∠BEC

⇒ a° + 26° = 49°

⇒ a° = 49 - 26 = 23°

Q2)

GIVEN :-

• ∠AED = 52°
• ∠EDB = 17°

TO FIND :-

• ∠CBD or ∠a

PROCEDURE :-

ABCD is a rectangle. In a rectangle , all the angles measure 90°. So,

∠ABC = 90°

⇒ ∠CBD + ∠DBE = 90°

⇒ ∠DBE = 90 - a

In a triangle , measure of an exterior angle of a triangle is the sum of the two opposite interior angles. So in ΔEBD ,

∠EBD + EDB = ∠AED

⇒ (90 - a)° + 17° = 52°

⇒ 107 - a = 52

⇒ -a = 52 - 107 = -55

(Multiplying -1 to both sides)

⇒ a = 55°