In Fig. 6.40, find the values of x, y and z

Solution:

In triangle ABD

Using the angle sum property

∠BAD + ∠BDA + ∠ABD = 180°

Substituting the values

60° + x + 60° = 180°

x + 120° = 180°

x = 180 - 120 = 60°

Using the exterior angle property

∠ADC = ∠BAD + ∠ABD

Substituting the values

y = 60 + 60 = 120°

In triangle ADC

Using the exterior angle property

∠ADB = ∠DAC + ∠DCA

x = 30° + z

Substituting the value of x

60° = 30° + z

z = 60° - 30°

z = 30°

Therefore, the values of x, y and z are 60°, 120° and 30°.

✦ Try This: In ∆PQR, if ∠P = ∠R, and exterior angle PQA = 150°, then find the angles of the triangle.

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

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NCERT Exemplar Class 7 Maths Chapter 6 Problem 129

In Fig. 6.40, find the values of x, y and z

Summary:

In Fig. 6.40, the values of x, y and z are 60°, 120° and 30°

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☛ Related Questions:

• If one angle of a triangle is 60° and the other two angles are in the ratio 1 : 2, find the angles
• In ∆PQR, if 3∠P = 4∠Q = 6∠R, calculate the angles of the triangle
• In ∆DEF, ∠D = 60°, ∠E = 70° and the bisectors of ∠E and ∠F meet at O. Find ∠F