Question

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Answer 1

Adjacent angles of parallelogram are equal to 180°

∴ ∠D + ∠C = 180°

⇒ z - 15 + 2z = 180

⇒ 3z - 15 = 180

⇒ 3z = 180 + 15

⇒ 3z = 195

z = 195/3

z = 65

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Finding the angles :-

∠D = z - 15

= 65 - 15

= 50°

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∠C = 2z

= 2( 65 )

= 130°

Opposite angles are equal in a parallelogram

∴ ∠D = ∠B and ∠C = ∠A

⇒ y = 50°

⇒ x = 130°

Answer 2

Answer:

The angles are -

• $\angle$ A = 130°
• $\angle$ B = 50°
• $\angle$ C = 130°
• $\angle$ D = 50°

Step-by-step-explanation:

First, know about all the properties of parallelogram -

1. Opposite sides are equal
2. Opposite angels are equal
3. Adjacent angles are supplementary
4. The diagonals of a parallelogram bisect each other.

______________________________

$\angle$ D + $\angle$ C = 180° .......... [ Adjacent angles are supplementary ]

$\implies$ z - 15 + 2z = 180

$\implies$ 3z - 15 = 180

$\implies$ 3z = 195

$\implies$ z = 195/3

$\implies$ z = 65

______________________________

As we are know to the Measure of z we can find the values of other angles :

Measure of $\angle$ D -

$\implies$ z - 15

$\implies$ 65 - 15

$\implies$ 50°

$\angle$ D = 50°

______________________________

Measure of $\angle$ C -

$\implies$ 2z

$\implies$ 2 × 65

$\implies$ 130°

$\angle$ C = 130°

______________________________

Angle D = Angle B ...... [ Opposite angels are equal ]

$\implies$ $\angle$ D = $\angle$ B

$\implies$ 50° = 50°

$\angle$ B = 50°

______________________________

Angle C = Angle A ...... [ Opposite angels are equal ]

$\implies$ $\angle$ C = $\angle$ A

$\implies$ 130° = 130°

$\angle$ A = 130°

______________________________

$\therefore$ The angles are -

• $\angle$ A = 130°
• $\angle$ B = 50°
• $\angle$ C = 130°
• $\angle$ D = 50°