Question

the sum of two opposite angles of a parallelogram is 130°. Find the measure of each angle.

Answer 1

Let Parallelogram be ABCD,

We are given ∠A + ∠C = 130° ..............................(1)

We know that, opposite ∠s of parallelogram are equal.

Hence, ∠A =  ∠C ......................................(2)

Hene, by using (1) and (2)

∠A + ∠A = 130°

2∠A = 130°

∠A = 65° = ∠C                [By using (2)]

Hence, measure of each angle is 65°

But, ∠A + ∠D = 180°

so, ∠D = ∠ B = 180° - 65° = 115°

Hence, all angles are

∠A = ∠C = 65

∠B = D = 115°

Answer 2

Given:-

• The sum of the opposite angles of a parallelogram is 130°

To Find:-

• The measures of each of its angle.

Solutions:-

• Let ABCD be a parallelogram
• Let the sum of its opposite angle be 130°

<A + <C = 130°

The opposite angle are equal in a parallelogram.

<A = <C = x°

⟹ x + x = 130°

⟹ 2x = 130°

⟹ x = 130/2

⟹ x = 65°

• <A = 65° and <C = 65°

⟹ <A + <B = 180° ⠀⠀⠀⠀⠀⠀⠀(the sum of adjacent angles of a parallelogram is 180°)

⟹ 65° + <B = 180°

⟹ <B = 180° - 65°

⟹ <B = 115°

• <B = <D = 115°
• (opposite angle of parallelogram are equal)

Hence, the measures of each angel are <A = 65°, <B = 115°, <C = 65° and <D = 115°.

Some Important:-

A parallelogram is a quadrilateral whose;

• Opposite sides are equal.
• Opposite sides are parallel.
• Opposite angles are equal.
• Adjacent angles sum up to 180°
• Diagonal bisect each other.