Question

Two angles form a linear pair. The measure of one angle is 24º more than the measure of the other angle. Find the measure of each angle.

Answer 1

Answer:

The measures of the two angles are 78° and 102°

Step-by-step explanation:

When two lines intersects at a point, then pairs of linear angles are formed

• The linear pair of angles are adjacent angles the sum of their measures is 180°

∵ The two angles form a linear pair

∴ The sum of the two angles = 180°

∵ The measure of one of them = 24° more than the measure

    of the other angle

→ Assume that the smaller one is x, then the greater one is

   x + 24, add them up and equate their sum by 180°

∵ x + x + 24 = 180

→ Add the like term in the left side

∴ 2x + 24 = 180

→ Subtract 24 from both sides

∴ 2x + 24 - 24 = 180 - 24

∴ 2x = 156

→ Divide both sides by 2

∴ 2x/2 = 156/2

∴ x = 78°

∴ The smaller angle = 78°

∵ The larger angle is x + 24

∴ The larger angle = 78 + 24 = 102°

The measures of the two angles are 78° and 102°