Answer:
- 5x+10° = 20°
- 10x +50° = 70°
Explanation:
You want the measures of the angles (5x+10°) and (10x+50°) that are divisions of an angle marked as a right angle.
Angle addition
The angle addition theorem tells you the whole is the sum of its parts. Here, the right angle in the diagram is divided into two parts, marked 5x+10° and 10x+50°. The measure of the right angle is the sum of these parts:
90° = (5x +10°) +(10x +50°)
30° = 15x . . . . . . . subtract 60°
2° = x . . . . . . . . . divide by 15
Using this value for x, we find the angle measures to be ...
5x+10° = 5(2°) +10° = 10° +10° = 20°
10x+50° = 10(2°) +50° = 20° +50° = 70°
In summary, ...
- 5x+10° = 20°
- 10x +50° = 70°