In Fig. 6.31(i), find the values of a, b and c.

Solution:

Given, the figure represents a triangle ABC.

We have to determine the values of a, b and c.

Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.

Considering triangle ABC,

By angle sum property,

∠A + ∠B + ∠C = 180°

90° + a + 70° = 180°

a + 160° = 180°

a = 180° - 160°

a = 20°

Considering triangle ABD,

∠BAD + ∠ABD + ∠BDA = 180°

30° + a + b = 180°

30° + 20° + b = 180°

50° + b = 180°

c = 180° - 50°

b = 130°

Considering triangle ADC,

∠ADC + ∠DAC + ∠ACD = 180°

c + 60° + 70° = 180°

c + 130° = 180°

c = 180° - 130°

c = 50°

Therefore, the values of a, b and c are 20°, 130° and 50°.

✦ Try This: Find the value of x.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

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NCERT Exemplar Class 7 Maths Chapter 6 Problem 109 (i)

In Fig. 6.31(i), find the values of a, b and c.

Summary:

In Fig. 6.31(i), the values of a, b and c are 20°, 130° and 50°.

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☛ Related Questions:

• In Fig. 6.31(ii), find the values of a, b and c
• In triangle XYZ, the measure of angle X is 30° greater than the measure of angle Y and angle Z is a . . . .
• In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than . . . .