Question

in the given fig, find the value of angle DAE​

Answer 1

Answer:

85°

Step-by-step explanation:

Given is that,

Angle ABC = 45°

Angle ACB = 105°

Angle CAD = 65°

To find the value of Angle DAE, we need to know the measure of Angle CAD, and Angle BAC.

Angle CAD is given but we need to find out Angle BAC.

In a ∆, sum of all the angles is 180°.

So in ∆ABC,

Angle ABC+ Angle ACB + Angle BAC = 180°

⇒45°+105°+ Angle BAC = 180°

⇒ 150°+ Angle BAC = 180°

⇒ Angle BAC = 180° - 150°

⇒ Angle BAC = 30°

As Angles CAD, Angle BAC, and Angle DAE lie on a straight line, their sum is 180°.

Angle CAD + Angle BAC + Angle DAE = 180°

⇒65°+30°+ Angle DAE = 180°

⇒95° + Angle DAE = 180°

⇒Angle DAE = 180° - 95°

⇒Angle DAE = 85°

Therefore, Angle DAE= 85°