Given:
Figure of similar triangles.
To find:
The value of x and the measure of NR.
Solution:
In triangle RST and RMN,
(Vertically opposite angles)
(Alternate interior angles)
(By AA property of similarity)
We know that, corresponding sides of similar triangles are proportional.




On further simplification, we get



The value of x is 7.
Now,




Therefore, the value of x is 7 and the measure of NR is 12 units.
1 way : 10d + 2d
another way: 5d + 5d + 2d
THEOREM:
- Angle sum property —: The sum of interior angles of a triangle is 180°.
ANSWER:
<u>By angle sum property</u>,
∠U + ∠V + ∠W = 180°
- 3x - 9° + 30° + 24° = 180°
- 3x + 45° = 180°
- 3x = 180° – 45°
- 3x = 135°
- x = 135/3
- x = 45°
So, <u>Correct choice</u> - [C] 45°.