Question

the difference of the measure two adjacent angles of a parallelogram is 50 find the measure of all its angles ​

Answer 1

ANSWER

The all the angles of the parallelogram are : 115°, 115°, 65° and 65°

EXPLANATION

Supplementary angle refers to the angle that sum up to 180°

Two adjacent angle of a parallelogram are supplementary.

Let one Angle of the parallelogram = a

the adjacent angle of ∠a = ∠b

According to the given info: ∠b = ∠a + 50°

⟹ ∠a + ∠b = 180°

⟹ ∠a + ∠a + 50° = 180°

⟹ 2∠a + 50° = 180°

⟹ 2∠a = 180°- 50°

⟹ 2∠a = 130°

⟹ ∠a = 130°/2

⟹ ∠a = 65°

Let's find the value of Angle b:

⟹ ∠b = ∠a + 50°

⟹ ∠b = 65° + 50°

⟹ ∠b = 115°

The two remaining angles are opposite to angle a and 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

⟹ 65° = ∠c

∠b = ∠d

⟹ 115° = ∠d

The all the angles of the parallelogram are : 115°, 115°, 65° and 65°

DOUBLE CHECK:

All the angles of the parallelogram should sum up to 360°

⟹ 115° + 115° + 65° + 65° ≟ 360°

⟹ 360° = 360°