Question

Q. In the adjoining figure angle POR and angle QOR form a linear pair-
(i) If a:b=2:3, find the values of a and b
(ii) If b-a=50°, find the values of a and b.
(iii) If 2a=b-30°, find the values of a and b​

Answer 1

Answer:

we solve all the above questions by linear equation a+b = 180°

Hope this will help you

Answer 2

Step-by-step explanation:

(i) a: b = 2 : 3

Let the angles be 2x and 3x.

a + b is a linear pair hence, a+ b = 180°

a + b = 180°

2x + 3x = 180°

5x = 180°

x = 180°/5

x = 36°

Angle a = 2x = 2* 36° = 72°

Angle b = 3x = 3 * 36° = 108°

Or,

Ratio  = 2 :3

Sum= 2+ 3 = 5

a + b = 180°

Angle a = 2/5 * 180° = 2 * 36° = 72°

Angle b = 3/5 * 180° = 3 * 36° = 108°

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(ii) b = a + 50°

a + b = 180°

a + (a+ 50°) = 180°

2a + 50° = 180°

2a = 180° - 50°

2a = 130°

a = 130°/2 = 65°

a+ b = 180°

65° + b = 180°

b = 180° - 65° = 115°

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(iii) 2a = b - 30°

      a = $\frac{b- 30}{2}$

a + b = 180°

b - 30° / 2 + b = 180°

b - 30° + 2b = 180° * 2

3b - 30° = 360°

3b = 360° + 30°

3b = 390°

b = 130°

a + b = 180°

a + 130° = 180°

a = 180° - 130°

a = 50°

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