Question

if one of the two opposite angle is 3x + 15 degree and other is 4x + 5 degree, then find all angles of the parallelogram?

Answer 1

Here we are given two opposite angles of a parallelogram:

3x + 15 and 4x + 5

We have to find all the angles

Properties of parallelogram:

1) Opposite angles are equal

2) The sum of adjacent angles is 180°

Keeping these properties in mind, we will solve this question

3x + 15 = 4x + 5

      x = 10

Therefore,

3x + 15 = 3(10) + 15

            = 45

4x + 5 = 4(10) + 5

         = 45

Now, the other two angles will be, 180 - 45 = 135

Therefore, the 4 angles of the parallelogram will be 45°, 45°, 135°, and 135°

     

Answer 2

Answer:

45°, 135°, 45°, 135°.

$\rule{70mm}{2pt}$

Step-by-step explanation:

GIVEN: One of the two opposite angle of parallelogram is (3x + 15)° and other is (4x + 5)°.

TO FIND: All angles of the parallelogram

Assumption: Let's say that the four angles of parallelogram are angle A, B, C and D.

$\rule{40mm}{2pt}$

SOLUTION:

Two opposite sides of a parallelogram are (3x + 15)° and (4x + 5)°. As angle A, B, C and D are the angles of parallelogram. So, we can say that angle A and C are opposite angles; while angle B and D are opposite to each other.

Therefore,

∠A = (3x + 15)° and ∠C = (4x + 5)°

We know that the opposite angles of parallelogram are equal. So,

→ ∠A = ∠C

Substitute the values,

→ 3x + 15° = 4x + 5°

→ 4x - 3x = 15° - 5°

→ x = 10°

Substitute value of x in (3x + 15)° and (4x + 5)°

→ 3(10°) + 15°

→ 30° + 15°

→ 45°

Similarly,

→ 4(10°) + 5°

→ 40° + 5°

→ 45°

From above too, it's clear that ∠A = ∠C = 45°.

Also, sum of two adjacent angles of a parallelogram is 180° (supplementary angles).

→ ∠A + ∠B = 180°

Substitute the values,

→ 45° + ∠B = 180°

→ ∠B = 180° - 45°

→ ∠B = 135°

Similarly, ∠D = 135°

Hence, all the angles of parallelogram are 45°, 135°, 45° and 135°.