Question

In triangle qst, where qst is an isosceles triangle and rt bisects angle t, what is true about angle qrt?

1) Angle qrt is acute
2) Angle qrt is obtuse
3) Angle qrt is right
4) Angle qrt is congruent to angle qst
5) Angle qrt is congruent to angle rst

Answer 1

In an isosceles triangle qst, angle qrt is acute as it is half the measure of angle qst.

Step-by-step explanation:

In an isosceles triangle qst, angle qst and angle stq are congruent since it is an isosceles triangle. Angle rtq bisects angle t, so angle rtq is half the measure of angle stq.

Since angle stq is congruent to angle qst, angle rtq is also half the measure of angle qst. Therefore, angle qrt is half the measure of angle qst and is acute because it is less than 90 degrees.