In a parallelogram ABCD if ∠ = 2 + 35!° and ∠# = 3 − 5!°.Find: (a) the value of x (b)measure of each angle of ABCD
Answers
Answered by
0
Answer:
We know that the opposite angles are equal in a parallelogram
Consider parallelogram ABCD
So we get
∠A=∠C=(2x−25)
o
∠B=∠D=(3x−5)
o
We know that the sum of all the angles of a parallelogram is 360
o
so it can be written as
∠A+∠B+∠C+∠D=360
o
By subtituting the values in the above equation
(2x+25)+(3x−5)+(2x+25)+(3x−5)=360
o
by addition we get
10x+40
o
=360
o
10x=320
o
x=32
o
now substituting the value x
∠A=∠C=(2x+25)
o
=(2(32)+25)
o
∠A=∠C=(54+25)
o
by addition
∠A=∠C=89
o
∠B=∠D=(3x−5)
o
=(3(32)−5)
o
∠B=∠D=(96−5)
o
by subtraction
∠B=∠D=91
o
therefore x=32
o
, ∠A=∠C=89
o
and ∠B=∠D=91
o
Similar questions