The measures of two adjacent angles of a parallelogram are in the ratio 4: 5. Find the measure of each of the angles of the parallelogram.
Answers
Answer:
Let ∠A and ∠B are two adjacent angles.
But we know that sum of adjacent angles of a parallelogram is 180o
∠A+∠B=180o
Given that adjacent angles of a parallelogram are in the ratio 4:5 and let that ratio be multiple of x
∠A+∠B=180o
4x+5x=180o
9x=180o
x=180/9
x=20o
∠A=4x=4×20=80o
∠B=5x=5×20=100o
Also ∠B+∠C=180o [Since ∠B and
∠C are adjacent angles]
100o+∠C=180o
∠C=180o−100o=80oNow, ∠C+∠D=180o [Since ∠C and
∠D are adjacent angles]
80o+∠D=180o
∠D=180o−80o=100o
Answer:
Let ∠A and ∠B are two adjacent angles.
But we know that sum of adjacent angles of a parallelogram is 180
o
∠A+∠B=180
o
Given that adjacent angles of a parallelogram are in the ratio 4:5 and let that ratio be multiple of x
∠A+∠B=180
o
4x+5x=180
o
9x=180
o
x=180/9
x=20
o
∠A=4x=4×20=80
o
∠B=5x=5×20=100
o
Also ∠B+∠C=180
o
[Since ∠B and
∠C are adjacent angles]
100
o
+∠C=180
o
∠C=180
o
−100
o
=80
o
Now, ∠C+∠D=180
o
[Since ∠C and
∠D are adjacent angles]
80
o
+∠D=180
o
∠D=180
o
−80
o
=100
o