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Answers
Answer:
Option (c) is your answer. This is given in my book too so jut told you the answer. I can't give you the explaination though, but it is the correct answer.
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Answer:
In ∆MFL,
By angle sum property of ∆,
angle F + angle L + angle LMF = 180°
30° + 90° + angle LMF = 180°
angle LMF = 180° - 120°
Angle LMF = 60°
Angle XMP = Angle LMF ( vertically opposite angles )
angle XMP = 60°
angle OPM = angle PXM + angle PMX ( exterior angle property of triangle )
angle OPM = 42° + 60°
angle OPM = 102°
In quadratilateral MNOP,
OP || MN
and ON || PM
therefore MNOP is a parallelogram.
In parallelogram,
opposite angles are equal.
therefore,
angle OPM = Angle ONM
angle ONM = 102°
ALPHA + BETA = 102° + 102°
= 204°