See explanation below
Step-by-step explanation:
From the question, we are told line TV is perpendicular to line US.
This means the point which they intersect has an angle of 90°.
We are also told line TV bisects STU.
For a line to bisect an angle, it means it divided the angle into two equal parts.
When line TV bisects STU, it divided it into angle STR and angle UTR
Hence, ∠STR = ∠UTR
Also line SU and line and line VT intersect to give vertical angles.
Angle R and the angle opposite it are vertical angles.
Vertical angles are equal.
The angle with 90° and the angle opposite it is also a vertical angle.
you can see from the illustration. The two angles opposite each other are equal to 90°.
Since angle on a straight line = 180°
angle R + 90° = 180°
angle R = 180-90
angle R = 90°
All the 4 angles that result from the intersection line VT and line SU are equal to 90°