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Class 8

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>>Parallelogram

>>In a parallelogram ABCD , if A = (2x +

Question



In a parallelogram ABCD, if ∠A=(2x+5)o and ∠B=(3x−5)o, find the value of x and the measure of each angle of the parallelogram.

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Solution



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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 360o

so it can be written as

∠A+∠B+∠C+∠D=360o

By subtituting the values in the above equation

(2x+25)+(3x−5)+(2x+25)+(3x−5)=360o

by addition we get

10x+40o=360o

10x=320o

x=32o

now substituting the value x

∠A=∠C=(2x+25)o=(2(32)+25)o

∠A=∠C=(54+25)o

by addition

∠A=∠C=89o

∠B=∠D=(3x−5)o=(3(32)−5)o

∠B=∠D=(96−5)o

by subtraction

∠B=∠D=91o

therefore x=32o, ∠A=∠C=89o and ∠B=∠D=91o

Answer:

Question - If one angle of a parallelogram is (2x-5)° and its adjacent angle is (3x-5)° then find all angles of the parallelogram.

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