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