Question

In a parallelogram ABCD, $\angle B$ is ${50^ \circ }$ more than $\angle A$. What is the measure of all the angles of parallelogram, ABCD?

Answer 1

Hint: In this question, a relation is given between two adjacent sides of a parallelogram. We also know that the sum of two adjacent sides of a parallelogram is ${180^ \circ }$. Using these two relations, we can make two equations. Then we can find the value of two angles as we have two equations using the substitution method and then we can find the rest of the angles.

Complete step by step answer:
In the above question, it is given that $\angle B$ is ${50^ \circ }$ more than $\angle A$. Here we have to find the measure of all the angles.

Therefore, we can write the above relation in the form of equation as:
$\angle B = \angle A + {50^ \circ }..........\left( 1 \right)$
We also know that the sum of two adjacent angles of a parallelogram is ${180^ \circ }$.Therefore,
$\angle A + \angle B = {180^ \circ }$
Now substitute the value of angle B in the above equation.
On substitution, we get
$\angle A + \angle A + {50^ \circ } = {180^ \circ }$
On simplification, we get
$ \Rightarrow 2\angle A + {50^ \circ } = {180^ \circ }$
On transposing, we get
$ \Rightarrow 2\angle A = {180^ \circ } - {50^ \circ }$
$ \Rightarrow 2\angle A = {130^ \circ }$

Now, dividing both sides by $2$
$ \Rightarrow \angle A = {65^ \circ }$
Now substitute the value of angle A in equation $\left( 1 \right)$
$\angle B = {65^ \circ } + {50^ \circ }$
$ \Rightarrow \angle B = {115^ \circ }$
We also know that
$\angle A = \angle C$(opposite angles of a parallelogram are equal)
$\angle B = \angle D$(opposite angles of a parallelogram are equal)
Therefore,
$ \Rightarrow \angle C = {65^ \circ }$
$ \therefore \angle D = {115^ \circ }$

Therefore, the angles of a parallelogram are ${65^ \circ }\,,\,{115^ \circ }\,,\,{65^ \circ }\,,\,{115^ \circ }.$

Note: In the above question, do not get confused about the larger angle between A and B. It is written that B is fifty degrees more than A. It means the measure of angle B is larger than A by fifty degrees. Here we have solved two equations by substitution method.We can also solve them with the help of the elimination method in which we either add or subtract both the equations simultaneously.