Q. 111

# In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.

Answer :

Given: ∠A is 40° less than ∠B

∠A is 50° less than ∠C

**Formula Used/Theory:-**

→ Angle sum property

Sum of all angles of triangle is 180°

Let ∠A be ‘x’

Then;

⇒ ∠A = ∠B - 40°

x = ∠B - 40°

∠B = x + 40°

⇒ ∠A = ∠C - 50°

x = ∠C - 50°

∠C = x + 50°

By angle sum property

∠A + ∠B + ∠C = 180°

x + (x + 40°) + (x + 50°) = 180°

3x + 90° = 180°

3x = 180° - 90° = 90°

x = = 30°

∠A = x

∴ ∠A = 30°

**Result:-** Measure of ∠A comes out to be 30°

Rate this question :

In a right-angled triangle, the angles other than the right angle are

NCERT - Exemplar MathematicsIn Fig. 6.34, find the measures of ∠PON and ∠NPO.

NCERT - Exemplar Mathematics

Find the values of x and y in Fig. 6.37. Plan a Strategy

NCERT - Exemplar Mathematics

In Δ ABC, if ∠A = ∠C, and exterior angle ABX = 140°, then find the angles of the triangle.

NCERT - Exemplar MathematicsIn a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.

NCERT - Exemplar MathematicsIn Fig. 6.31(i) and (ii), find the values of a, b and c.

NCERT - Exemplar Mathematics

In Fig. 6.30, find the value of x.

NCERT - Exemplar Mathematics

The measure of three angles of a triangle are in the ratio 5 : 3 : 1. Find the measures of these angles.

NCERT - Exemplar Mathematics