Question

Point O is the incenter of triangle ABC.

Point O is the incenter of triangle A B C. Lines are drawn from the points of the triangle to point O. Lines are drawn from point O to the sides of the triangle to form right angles and line segments O Q, O R, and O S. Angle O B C is 15 degrees. Angle O C R is 30 degrees.
What is mAngleQOB?

30°
60°
75°
90°

Answer 1

75°

Reason: O is the incenter, so OB and OC bisect ∠B and ∠C. Given ∠OBC = 15°, so ∠B = 30°. Given ∠OCR = 30°, so ∠C = 60°. Hence ∠A = 90°. OQ is perpendicular to BC, so the angle between OQ and OB is 90° − ∠OBC = 90° − 15° = 75°.