In the given figure line AB and CD intersect at O. angle BOC = 36°. Find angle x ,angle y & angle z.
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In the given figure line AB and CD intersect at O. angle BOC = 36°. Find angle x ,angle y &
In the given figure line AB and CD intersect at O. angle BOC = 36°. Find angle x ,angle y & angle z.
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Step-by-step explanation:
In first figure,
∠AOD=∠BOC ------- Vertically Opposite angles
∴x=36∘
∠AOC+∠COB=180∘ ------ Angles on straight line
y+36∘=180∘
y=180∘−36∘
y=144∘
∠AOC=∠BOD ------- Vertically Opposite angles
y=z=144∘
In second figure,
∠POR+∠ROT+∠QOT=180∘ ------ Angles on straight line
2x+90∘+x=180∘
3x=90∘
x=30∘
∴2x=60∘
∠POR=∠SOQ ------- Vertically Opposite angles
2x=y=60∘
∠POS=∠ROQ ------- Vertically Opposite angles
z=90∘+x
z=90∘+30∘
z=120∘
Verified answer
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Math ex-12(A), Question-11