Question

parallelogram.
& If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram​

Answer 1

ANSWER

108°, 72°, 108° and 72° are all the angles of the parallelogram.

EXPLANATION:

Given

• The shape is a parallelogram.
• one angle of a parallelogram is two third of its adjacent angle.

To Find

• All the angles of the parallelogram.

Solution

Let one angle of the parallelogram = a

Adjacent angle of angle a = b

Adjacent angle of angle a = 2a/3

Adjacent angles of a parallelogram are supplementary. that is they some up to 180°

The equation becomes:

⟹ a + b = 180°

⟹ a + 2a/3 = 180°

⟹ (3a + 2a)/3 = 180°

⟹ 3a + 2a = 180° × 3

⟹ 5a = 540^

⟹ a = 540°/5

⟹ a = 108°

The adjacent angle of a:

⟹ 2a/3

⟹ 2/3 × 108°

⟹ 72°

The remaining two angles are the opposite angles a and its adjacent, angle b

Let the angle opposite to a = c

Let the angle opposite to b = d

Opposite angles of a parallelogram are equal.

⟹ a = c

⟹ 108° = c

⟹ b = d

⟹ 72° = d