Question

ABC is a triangle in which BE is perpendicular to AC and CD is perpendicular to AB & BE and CD intersect at O. If BAC=75 o, then the measure of angle BOC is

Answer 1

Answer:

If BAC=75 o, then the measure of angle BOC is. 2. See answers.

Answer 2

Answer:

The measure of ∠BOC = 105°

Step-by-step explanation:

Given,

In triangle ABC,

BE is perpendicular to AC and CD is perpendicular to AB

BE and CD intersect at O

∠BAC = 75°

To find,

The measure of ∠BOC

Solution:

Recall the concepts:

Sum of four angles of a quadrilateral is 360°

Vertically opposite angles are equal

Since BE is perpendicular to AC, ∠BEA = 90°

Since CD is perpendicular to AB, ∠CDA = 90°

Then from the Quadrilateral AEOD, we have

∠DAE + ∠AEO + ∠EOD + ∠ODA  = 360°(since sum of four angles of a quadrilateral is 360°)

Here

∠DAE = ∠BAC = 75°

∠AEO = ∠BEA = 90°

∠ODA = ∠CDA = 90°

Substituting these values we get,

75+90+ ∠EOD+90 = 360

∠EOD +255 = 360

∠EOD = 360 -255

= 105

∠EOD = 105°

∠BOC = 105°, (Since ∠EOD, ∠BOC are vertically opposite angles)

∴ The measure of ∠BOC = 105°

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