Question

given the parallelogram ABCD, solve for X when angle A equals (30+ 5x)° and angle D equals (15+10x)° degrees. Also, sides AB and CD opposite each other.

Answer 1

X = 9°

Explanation:

In parallelogram, the sum of the adjacent angles is equal to 180°

Given two adjacent angles of a parallelogram

<A = (30+ 5x)° and <D = (15+10x)°

To get X, we will take the sum of this two angles and equate it to 180°

<A + <D = 180°

(30+5x)° + (15+10x)° = 180°

Expanding the bracket

30+5x+15+10x = 180°

45+15x = 180°

15x = 180-45

15x = 135°

x = 135/15

x = 9°

Answer 2

Answer: The value of x = 9.

Explanation:

Since we have given that

∠A = (30+5x)°

∠ D = (15+10x)°

Since ABCD is a parallelogram.

In parallelogram, opposite angles are equal and sum of adjacent angle is supplementary angles.

So, ∠A + ∠D = 180° (∵ A and D are adjacent angles)

`30+5x+15+10x=180^\circ\\\\45+15x=180^\circ\\\\15x=180^\circ-45^\circ\\\\x=(135)/(15)\\\\x=9`

Hence, the value of x = 9.