c) In a pentagon, two angles are 50° and 80°, and the other three angles are
in the ratio of 2:3:5. Find the measure of the largest and the
smallest angle.
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Answer:
Given ratio of angles of quadrilateral ABCD is 2:3:5:8
Let the angles of quadrilateral ABCD be 2x,3x,5x,8x, respectively.
We know, by angle sum property, the sum of angles of a quadrilateral is 360
o
.
⇒2x+3x+5x+8x=360
o
⇒18x=360
o
∴x=20
o
.
∴∠A=2x=2×20
o
=40
o
,
∠B=3x=3×20
o
=60
o
,
∠C=5x=5×20
o
=100
o
and ∠D=8x=8×20
o
=160
o
.
∴ The smallest angle =40
o
.
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