Question

b) The sum of the two opposite angles of a parallelogram is 140°.find all the angles of the parallelogram ​

Answer 1

Answer:

since opposite angles of parallelogram are equal,

let one angle be x

then ,

$x + x = 140 \\ 2x = 140 \\ x = 140 \div 2 \\ x = 70$

now , adjacent angles of a parallelogram are supplementary

so, let another adjacent angle to x be y

then,

$x + y = 180 \\ 70 + y = 180 \\ y = 180 - 70 \\ y = 110$

hence, if there is a parallelogram ABCD

then angle A = Angle C=70⁰

& Angle B =Angla D = 110⁰

Answer 2

First off, we must understand that in a parallelogram, opposite angles are equal.

Given, Sum of 2 opp. angles = 140⁰

Let the one angle be "x"

--> x + x = 140⁰

--> 2x = 140⁰

∴ x = 70⁰

Now, if one angle is 70⁰, we know that the angle adjacent to it is supplementary.

Take this adjacent angle to be "y"

So, 70⁰ + y = 180⁰

--> y = 180⁰ - 70⁰

∴ y = 110⁰

As I mentioned in the first statement, opposite angles are equal. So, this means that the angle opposite to y is also 110⁰.

∴ Angles are 70⁰, 110⁰, 70⁰,

110⁰