Math, asked by slytherine0ind, 5 months ago

<ACD is an exterior angle of ∆ABC, if <ACD = 110°,<A = 60° then <B = ?​

Answers

Answered by Ladylaurel
4

Answer :

The measure of ∠B is 10°.

Step-by-step explanation :

To Find,

  • ∠B of ∆ABC

Solution,

Given that,

  • ∠ACD is an exterior angle of ∆ABC
  • ∠ACD = 110°
  • ∠A = 60°

Figure,

  • Refer the attachment

A . T . Q

To get the measure of ∠B, First we need to find out the measure of ∠C [ ∠C = 180° - ∠ACD ], Hence, the measure of ∠C is,

➜ ∠C = 180° - ∠ACD

➜ ∠C = 180° - 110°

➜ ∠C = 70°

Now, we we can get the measure of ∠B the angle sum property of triangle.

Let us assume ∠B as ∠B,

➜ ∠A + ∠B + ∠C = 180°

➜ 60° + ∠B + 110° = 180

➜ 170° + ∠B = 180°

➜ ∠B = 180° - 170°

➜ ∠B = 10° ★

Hence, the measure of ∠B is 10°.

Now, Verification

➜ ∠A + ∠B + ∠C = 180°

➜ 60° + 10° + 110° = 180°

➜ 70 + 110 = 180

➜ 180 = 180

L.H.S = R.H.S

HENCE, VERIFIED !

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