Question

in a parallelogram pqrs ∠p = (3a-10°) ∠q(5a+30°) find the all angles of the parallelogram.

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Answer 1

Step-by-step explanation:

Given:

In a parallelogram PQRS:

∠p = (3a - 10)°

∠q = (5a + 30)°

To find:

All the angles of the parallelogram.

Solution:

In a parallelogram,

• Adjacent angles are supplementary.

Therefore,

• ∠p + ∠q = 180°

⇒ (3a - 10)° + (5a + 30)° = 180°

⇒ 3a - 10° + 5a + 30° = 180

⇒ 8a + 20° = 180°

⇒ 8a = 160°

∴ a = 20°

Measures of angles:

∠p [3a - 10]° = 60° - 10° = 50°

∠q [5a + 30°] = 100° + 30° = 130°

We know,

• Opposite angles are equal in a parallelogram.

∠p = ∠r = 50°

∠q = ∠s = 130°

Measure of all the angles:

• ∠p = 50°, ∠q = 130°, ∠r = 50°, ∠s = 130°.

Verification:

• Sum of all the angles in a quadrilateral is equal to 360°.

∠p + ∠q + ∠r + ∠s = 360°

⇒ 50° + 130° + 50° + 130° = 360°

⇒ 260° + 100° = 360°

⇒ 360° = 360°

∴ L.H.S = R.H.S

Alternate method:

We know,

• Sum of all the angles in a parallelogram is equal to 360°.

We have,

• ∠p = (3a - 10)°
• ∠q = (5a + 30)°

We know,

• Opposite angles in a parallelogram are equal.

∠p = ∠r

∠q = ∠s

Hence,

• (3a - 10)° + (5a + 30)° + (3a - 10)° + (5a + 30)° = 360°

⇒ 3a - 10 + 5a + 30 + 3a - 10 + 5a + 30 = 360°

⇒ 16a - 20 + 60 = 360°

⇒ 16a + 40° = 360°

⇒ 16a = 320°

∴ a = 20°

Measures of angles:

∠p [3a - 10]° = 60° - 10° = 50°

∠q [5a + 30°] = 100° + 30° = 130°

∠r [3a - 10]° = 60° - 10° = 50°

∠q [5a + 30°] = 100° + 30° = 130°

Answer 2

Step-by-step explanation:

given :

in a parallelogram pqrs ∠p = (3a-10°) ∠q(5a+30°) find the all angles of the parallelogram.

to find :

find the all angles of the parallelogram.

solution :

• P+q=180

• 3a-10+5a+30=180

• a=20

• P =r=50

• Q=s=130