Geometry and TrigonometryVery hardAngle between a bisector and a side
Geometry and Trigonometry practice question
In triangle RST, RS = RT and angle S measures 36°. The bisector of angle R meets ST at U. What is the measure, in degrees, of angle RUS?
Answer: 90
Angle R is 108°, its bisector makes angle SRU 54°, and in triangle RSU the third angle is 180 − 36 − 54 = 90.
Common wrong answers
- If you answered 54
- 54 is angle SRU.
- If you answered 72
- 72 is angle T's supplement of 108, not angle RUS.
- If you answered 108
- 108 is angle R.
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