Question

Two adjacent angles of a parrallelogram are (3x-4)and (3x+10) .find the measure of these angles of the parrallelogram.

Answer 1

Answer:-

83° and 97°

Given :-

(3x - 4)°

(3x + 10)°

To find :-

The measure of these angles.

Solution:-

Parallelogram → A quadrilateral having opposite sides parallel and equal and diagonal bisect each other.

• The measure of adjacent angle of parallelogram is 180°.

• The opposite angle of a parallelogram is equal.

→$(3x -4) +(3x+10) = 180^{\circ}$

→$3x -4 +3x +10 = 180$

→$6x +6 = 180$

→$6x = 180-6$

→$6x = 174$

→$x = \dfrac{174}{6}$

→$x = 29$

• The angles of parallelogram are :-

→3x - 4

→3 × 29° - 4

→87 - 4

→83°

→3x + 10

→3 × 29 + 10

→87 + 10

→97°

hence,

The measure of all angles of parallelogram are 83° , 83° , 97° ,97°

Answer 2

Given :-

• Two Adjacent angles of parallelogram :-

• 3x - 4
• 3x + 10

To Find :-

• Measure of all the angles.

Solution :-

Let ABCD be the parallelogram and,

∠A = (3x + 10)

∠D = (3x - 4)

Now,

(3x + 10) + (3x - 4) = 180° (Adjacent angles are supplementary)

Finding value of x

(3x + 10) + (3x - 4) = 180

3x + 3x + 10 - 4 = 180

6x + 6 = 180

6x = 180 - 6

6x = 174

x = 174/6

x = 29

Finding measure of angles

(3x + 10) = 3(29) + 10 = 97

(3x - 4) = 3(29) - 4 = 83

-------------------------

• ∠A = 97°

• ∠D = 83°
• ∠C = 97° (Opposite angles are equal)
• ∠B = 83°