Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

In ΔABC, AB = AC, O is a point at BC such that BO = OC and OD is perpendicular to AB and OE is perpendicular to AC. If ∠BOD = 40°, then the measure of ∠AOE is ?

Options:

50°

75°

60°

90°

Correct Answer:

50°

Explanation:

In ΔBOD

∠DBO = 180° - 90° - 40° = 50°

AB = AC

∴ ∠ABO = ∠ACO = 50°

In ΔCOE

∠EOC = 180° - 50° - 90° = 40°

∠DOE = 180° - 80° = 100°

\(∠AOE=\frac{100°}{2}=50°\)