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°
