Question

The sum of two opposite angles of a parallelogram is 130º. Find all the angles of the
parallelogram.​

Answer 1

Answer:

ang A = ang C = 65°

ang B = ang D = 115°

Step by Step answer :

Let ABCD be the parallelogram

Let A and C be the given opposite sides

Therefore /_ A + /_ C = 130

2 /_ A = 130

/_ A = 130 / 2

/_ A = 65°

Hence /_ A = /_C = 65°

Now we know that in a parallelogram adjacent angles are supplementary

/_ A + /_ B = 180

/_ B = 180 – 65

/_ B = 115°

Also

/_ B = /_ D = 115° ( opposite angles are equal )

Answer 2

Given

Sum of two opposite angles is 130°

To Find

Measure of all angles of parallelogram

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Let ABCD is a parallelogram

According to the question

∠A+∠C=130°

∠A=∠C [Opposite sides and angles of a parallelogram are equal]

∠A=∠A [∵∠A=∠C then we can replace ∠C with ∠A or ∠A=∠A]

Now,∠A+∠A=130°

2∠A=130°

∠A=65°

∠A+∠B=180°[ adjacent sides make supplimentry angles]

65°+∠B=180°

∠B=115°

Now,∠A=∠C & ∠B=∠D

∴ ∠A=65°;∠B=115°;∠C=65° & ∠D=115°