Question

In triangle ABC; if angle A = 85 degree and exterior of angle C = 120degree; then find angle B​

Answer 1

✬ Angle B = 35° ✬

Step-by-step explanation:

Given:

• Meaure of angle A is 85°.
• Measure of exterior angle C is 120°.

To Find:

• What is the measure of angle B ?

Solution: In ∆ABC we have

• ∠A = 85°
• ∠ACX = 120°

Here ∠ACB and ∠ACX are linear pair angles.

As we know that

★ Sum of Linear pair angles = 180° ★

$\implies{\rm }$ ∠ACB + ∠ACX = 180°

$\implies{\rm }$ ∠ACB + 120° = 180°

$\implies{\rm }$ ∠ACB = 180° – 120°

$\implies{\rm }$ ∠ACB = 60°

Now, in ∆ABC by angle sum property

$\implies{\rm }$ ∠A + ∠B + ∠C = 180°

$\implies{\rm }$ 85° + ∠B + 60° = 180°

$\implies{\rm }$ 145° + ∠B = 180°

$\implies{\rm }$ ∠B = 180° – 145°

$\implies{\rm }$ ∠B = 35°

Hence, measure of angle B is 35°.