In Fig. 5.14, POQ is a line. If x = 30°, then ∠ QOR is
a. 90°
b. 30°
c. 150°
d. 60°

Solution:

Given, POQ is a line.

x = 30°

We need to find the measure of ∠QOR.

We know that the sum of angles on a straight line is always equal to 180 degrees.

So, ∠ POS + ∠SOR + ∠QOR = 180°

From the figure,

x + 2y + 3y = 180°

30° + 2y + 3y = 180°

30° + 5y = 180°

5y = 180° - 30°

5y = 150°

y = 150°/5

y = 30°

∠QOR = 3y

∠QOR = 3(30°)

∠QOR = 90°

Therefore,∠ QOR = 90°

✦ Try This: The measure of an angle which is three times its complement is

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5

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NCERT Exemplar Class 7 Maths Chapter 5 Problem 14

In Fig. 5.14, POQ is a line. If x = 30°, then ∠ QOR is: a. 90°, b. 30°, c. 150°, d. 60°

Summary:

POQ is a line. If x = 30°, then ∠QOR is 90°

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☛ Related Questions:

• The measure of an angle which is four times its supplement is: a. 36°, b. 144°, c. 16°, d. 64°
• In Fig. 5.15, the value of y is: a. 30°, b. 15°, c. 20°, d. 22.5°
• In Fig. 5.16, PA || BC || DT and AB || DC. Then, the values of a and b are respectively: a. 60°, 120 . . . .