# Find the values of the angles x, y and z in each of the following:

**Solution:**

We use the geometry concepts like supplementary angles, vertically opposite angles and adjacent angles to solve the problem.

There are two operations done in sequence. First, if one angle is 55° then the angle opposite to it will also be 55° as vertically opposite angles are equal.

Also sum of ∠x + ∠y = 180° and ∠z + 55° = 180°.

Solve for ∠x, ∠y, ∠z:

(i) ∠x = 55° (Vertically opposite angle)

∠x + ∠y = 180°(Linear pair)

55 °+ ∠y = 180°

∠y = 180°- 55 °

∠y = 125 °

Therefore, ∠y = ∠𝑧 = 125°(Vertically opposite angle) Hence, ∠x = 55° , ∠y= 125°, ∠z = 125°

(ii) By using the angle sum property, find the value of x, and then find the value of 𝑦 and 𝑧. Since the sum of 𝑦 + z = 180°. Now, it’s a matter of finding 𝑦 𝑎𝑛𝑑 𝑧.

By using angle sum property,

40° + 𝑥 + 25° = 180°(Angles on straight line)

x + 65° = 180°

x = 180° - 65° = 115°

Also, 40° + 𝑦 = 180°(Linear pair)

𝑦 = 180° − 40°

𝑦 = 140°

𝑦 + 𝑧 = 180°(Linear pair)

140° + 𝑧 = 180°(𝑦 = 140°)

𝑧 = 180°- 140°

𝑧 = 40°

Thus, 𝑥 = 115°, 𝑦 = 140° and 𝑧 = 40°

**Video Solution:**

## Find the values of the angles x, y and z in each of the following:

### NCERT Solutions for Class 7 Maths - Chapter 5 Exercise 5.1 Question 12

Find the values of the angles x, y and z in each of the following:

𝑥 = 115° 𝑦 = 140° and 𝑧 = 40°