Step-by-step explanation:
<TUV = 8x -8°
<STU = 67°
<TSU = 5x - 15°
Now
<TUV = <STU + <TSU <exterior angle of a triangle is equal to the sum of two opposite interior angle >
8x - 8° = 67° + 5x -15°
8x - 5x = 67° - 15° + 8°
3x = 60°
Therefore x = 20°
<TUV = 8 *20° - 8° = 160°-8° = 152°
Answer: TUV = 36 degrees
Step-by-step explanation:
The sum of the angles in a straight line is 180 degrees. It means that
Angle TUS + angle TUV = 180
TUS + 8x - 8 = 180
TUS = 180 + 8 - 8x
TUS = 188 - 8x
Also, the sum of the angles in a triangle is 180 degrees. It means that
61 + 5x - 15 + TUS = 180
TUS = 180 + 15 - 61 - 5x
TUS = 134 - 5x
Therefore,
188 - 8x = 134 - 5x
- 5x + 8x = 188 - 134
3x = 54
x = 54/3
x = 18
Therefore,
TUV = 8x - 8 = (8 × 18) - 8 = 136 degrees
