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Maths-

General

Easy

Question

In $straight triangle ABC comma space straight angle straight A plus straight angle straight B equals 70 to the power of ring operator$ and $straight angle straight B plus straight angle straight C equals 135 to the power of ring operator$ . Hence find the measure of each angle

hint Hint:

Find ∠B by using the given equations and sum of angles in triangle .
We get value of ∠B ,substitute in the given equations to get the value of other angles

The correct answer is: ∠ A = 45° ∠ B = 25° ∠ C = 110°

Step 1:- Find ∠B
Given , ∠A + ∠B = 70° ; ∠B + ∠C =135°
Adding both equations give ∠A + 2 ∠B + ∠C = 70° + 135° = 205° —-Eq1
But in ABC ,∠ A + ∠B + ∠C =180°—-Eq2
Eq2-Eq1 we get ∠ B = (205-180)°= 25°
∠B= 25°
Step 2:- Find ∠A and ∠C
Substitute the value of angle B in the given equations
∠A +∠ B = 70° $not stretchy rightwards double arrow$ ∠A + 25° = 70° $not stretchy rightwards double arrow$ ∠A = 70°-25° $not stretchy rightwards double arrow$ ∠A = 45°
∠B + ∠C = 135° $not stretchy rightwards double arrow$ ∠C + 25° = 135° $not stretchy rightwards double arrow$ ∠C = 135°-25° $not stretchy rightwards double arrow$ ∠C = 110°

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