Question

Given the figure below, find the values of x and z .

There is a picture below to see it clearly.

Answer 1

Z and 96 are vertical angles so they equal each other. The other angle makes a straight line with the 96 degree angle so subtract from 180 to find the measure of that angle is 84. Set the expression equal to 84 and solve.

Answer 2

Two angles whose sum is 180° are called supplementary angles. The value of x is 10, while the value of z is 96.

What are supplementary angles?

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

The measure of ∠Z will be equal to 96° because ∠AOB and ∠COD are vertically opposite angles.

The sum of the measure of ∠AOB and ∠BOC will be equal to 180°, since both lie on the same line, therefore,

∠AOB + ∠BOC = 180°

96° + (14x - 56)° = 180°

14x - 56 = 180 - 96

14x = 140

x = 10°

Hence, the value of x is 10, while the value of z is 96.

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