A side of the triangle below has been extended to form an exterior angle of 67°. Find the value of xx.
52°
67°
x°
Answer
Attempt 1 out of 2
To find the value of x, we must first recognize that the sum of the interior angles of a triangle is always 180°.
Since one exterior angle is 67°, the corresponding interior angle is 180° - 67° = 113°.
Now, we see that the two angles given in the triangle are 52° and x°. Therefore, the sum of all three angles must be 52° + 113° + x° = 180°.
Solving for x, we get:
52° + 113° + x° = 180°
165° + x° = 180°
x° = 180° - 165°
x° = 15°
Therefore, the value of x is 15°.