in figure three lines p,q,and r are concurrent at o if a equal to 50°and b equal to 90° find c,d,e,and f
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Answered by
37
Given: Three coplanar lines AB, CD and PQ meet at O.
∠ BOQ = a = 50° and ∠ BOC = b = 90°
To find: c, d, e and f.
Proof: Adjacent angles, ∠ BOQ, ∠ BOP form a linear pair. ... ∠ BOQ + ∠ BOP = 180° (Linear Pair Axiom)
a + ∠ BOC + ∠ COP = 180°
a + b + c = 180°
50° + 90° + c = 180° (given)
c = 180°- (90° + 50°)
= 180° - 140° = 40° d = a = 50° (Vertically opp. angles)
e = b = 90° (Vertically opp. angles)
f = c = 40° (Vertically opp. angles).
Answered by
7
Step-by-step explanation:
Given a=50
o
,∴f=40
o
(a+f=90
o
)
b=90
o
f=c=40
o
[vertically opposite angles]
∴d=90−40=50
o
e=90
o
(a+b+c+d+e+f=360
o
)
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