Question

# In the given figure; AOC is a straight line. If angle AOB =50∘, angle AOE =90∘ and angle COD=25∘; find the measure of: (1) angle BOC (2) angle EOD (3) obtuse angle BOD (4) reflex angle BOD

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Solution

## (1) Given AOC is a straight line ∠AOB=50∘∠AOE=90∘∠COD=25∘ To find the measure of ∠BOC, ∠AOB+∠BOC=180∘ (Linear pair of angle ) 50∘+∠BOC=180∘ Our further calculation, we get ∠BOC=180∘−50∘ ∠BOC=130∘ (2) To find the measure ∠EOD∠EOD+∠COD=90∘(Since ∠AOE=90∘)∠EOD+25∘=90∘∠EOD=90∘−25∘We get,∠EOD=65∘ (3) To find the measure of obtuse angle BOD, ∠BOD=∠BOC+∠CODSubstituting the value of ∠BOC and ∠COD,We get,∠BOD=130∘+25∘We get,∠BOD=155∘ (4) To find the measure of reflex angle BOD reflex ∠BOD=360∘−∠BOD=360∘−155∘We get,reflex∠BOD=205∘

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