(3x+70)` and (x+100)` represent two vertically opposite angles. Find the measure of each of the two angles.

Solution:

As we know thattwo pairs of angles are formed by two intersecting lines. Vertical angles are opposite angles in such an intersection. Vertical angles are equal to each other.

Then the equation we get :

(3x + 70)o = (x + 100)o

3x + 70 = x + 100

3x - x = 100 - 70

2x = 30

x = 30/2 = 15

Then the measure of the two angles = (3x + 70)o =(3 x 15 + 70)o = 115o, (x + 100)o = (15 + 100) = 115o.

Ans: 115o.

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