In ∆ ABC, DE || BC (Fig. 6.39). Find the values of x, y and z.

Solution:

Given, ABC is a triangle

Also, DE || BC

We have to find the values of x, y and z.

Considering triangle ABC,

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

By angle sum property,

∠A + ∠B + ∠C = 180°

z + 30° + 40° = 180°

z + 70° = 180°

z = 180° - 70°

z = 110°

Since DE || BC, the corresponding angles are equal.

So, ∠ADE = ∠ABC

x = 30°

Similarly, ∠AED = ∠ACB

y = 40°

Therefore, the values of x, y and z are 30°, 40° and 110°.

✦ Try This: The angles of a triangle are arranged in ascending order of their magnitudes. If the difference between two consecutive angles is 15°, find the three angles.

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

NCERT Exemplar Class 7 Maths Chapter 6 Problem 128

In ∆ ABC, DE || BC (Fig. 6.39). Find the values of x, y and z.

Summary:

In ∆ ABC, DE || BC (Fig. 6.39). The values of x, y and z are 30°, 40° and 110°.

☛ Related Questions:

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