the sum of the measure of two angle is 100°and their diffraance is 2πc/9 find angle in radian measure
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Answer:
Let ∠A=
9
2π
=
9
2π
×
π
180
o
=40
o
Let measures of other angles be 3x,5x and 8x.
Let, ∠B=3x,∠C=5x and ∠D=8x
We know that sum of four angles of an quadrilateral is 360
o
.
∴ ∠A+∠B+∠C+∠D=360
o
.
⇒ 40
o
+3x+5x+8x=360
o
.
⇒ 16x=320
o
.
⇒ x=20
o
.
Now
∠B=3x=3×20
o
=60
o
∠C=5x=5×20
o
=100
o
∠D=8x=8×20
o
=160
o
.
Measure in radian,
∠B=60
o
×
180
o
π
=
3
π
∠C=100
o
×
180
o
π
=
9
5π
∠D=160
o
×
180
o
π
=
9
8π
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