Since the exterior angle of a triangle is equal to the sum of its adjacent interior angles, we can subtract the given 127° from 180° to find the measure of the corresponding interior angle:
180° - 127° = 53°
This angle is opposite to the side of length x, so we can use the sine ratio to find x:
sin 53° = x / (10 + x)
Cross-multiplying, we get:
x = (10 + x) sin 53°
Expanding:
x = 10 sin 53° + x sin 53°
Subtracting x sin 53° from both sides:
x - x sin 53° = 10 sin 53°
Factoring out x:
x (1 - sin 53°) = 10 sin 53°
Dividing both sides by (1 - sin 53°):
x = 10 sin 53° / (1 - sin 53°)
Using a calculator:
x ≈ 17.6
Therefore, the value of x is approximately 17.6 units.
A side of the triangle below has been extended to form an exterior angle of 127°. Find the value of x
1 answer