Question

the defference in the measure of two supplementary angles is 30. find the measure of the angles​

Answer 1

Step-by-step explanation:

let the angle be x and supplementary angle be 180-x

so given, ( 180 -x )- x = 30

-x-x =30 - 180

-2x= -150

now minus from both sides will be cancelled

2x=150

so x=150/2=75

angle =75

supplementary angle =180-75=105

Answer 2

Answer:

The angles are 75° and 105°.

Step-by-step explanation:

Gívєn -

Difference between the two Supplementary angles = 30°

Tσ fínd -

The measure of the angles

Sσlutíσn -

Let the angles be as -

• One as x
• Second as y

$\rule{300}{1.5}$

As given in the Question, the Difference between the angles is 30°.

$\sf{\implies} \: x - y = {30}^{\circ}$

$\sf{\implies} \: x = 30 + y \: .....(Equation \: 1)$

Supplementary angles are the angles which when added, their sum is 180°.

$\sf{\implies} \: x + y = {180}^{\circ}$

$\sf{\implies} \: (30 + y) + y = {180}^{\circ}$

$\sf{\implies} \: 30 + y + y = {180}^{\circ}$

$\sf{\implies} \: 30 + 2y = {180}^{\circ}$

$\sf{\implies} \: 2y = 180 - 30$

$\sf{\implies} \: 2y = {150}^{\circ} \:$

$\sf{\implies} \: y = \dfrac{150}{2}$

$\sf{\implies} \: y = 75$

One Angle = 75°

$\rule{300}{1.5}$

Second Angle =

$\sf{\implies} \: x = 30 + y$

$\sf{\implies} \: x = 30 + 75$

$\sf{\implies} \: x = {105}^{\circ}$

$\therefore$ The angles are 75° and 105°.