Question

Two angles are supplementary, and one is 10 degrees more than another. What is the size of each angle?

Answer 1

Given :-

In two Supplementary angles, One angle is 10° more than the other .

To find :-

The measure of each angle.

Solution :-

Given that

Two angles are Supplementary.

Let the other angle be X°

The supplementary angle of X° = (180-X)°

According to the given problem

One angle = 10° more than the other

=> (180-X)° = X° +10°

=> 180°-10° = X° +X°

=> 170° = 2X°

=> 2X° = 170°

=> X° = 170°/2

=> X° = 85°

Therefore, X = 85°

The other angle = 85°

One angle = 85°+10° = 05°

Answer:-

The measure of the two Supplementary angles are 95° and 85°

Points to know:-

• The sum of two angles is 180° are called Supplementary angles.

Ex :- (100°,80°) , (60°,120°),...

• The supplementary angle of X° = (180-X)°

Ex:- Supplementary angle of 70° = 180°-70° = 110°

Answer 2

Answer:

Given :-

• Two angles are supplementary, and one is 10° more than another.

To Find :-

• What are the angles.

Solution :-

Let,

$\mapsto \bf First\: Angle =\: x$

$\mapsto \bf Other\: Angle =\: x + 10^{\circ}$

As we know that :

$\small \bigstar \: \: \sf\boxed{\bold{\pink{Sum\: of\: Supplementary\: Angles =\: 180^{\circ}}}}\: \: \: \bigstar$

According to the question by using the formula we get :

$\implies \sf x + (x + 10^{\circ}) =\: 180^{\circ}$

$\implies \sf x + x + 10^{\circ} =\: 180^{\circ}$

$\implies \sf 2x + 10^{\circ} =\: 180^{\circ}$

$\implies \sf 2x =\: 180^{\circ} - 10^{\circ}$

$\implies \sf 2x =\: 170^{\circ}$

$\implies \sf x =\: \dfrac{170^{\circ}}{2}$

$\implies \sf\bold{\blue{x =\: 85^{\circ}}}$

Hence, the required angles are :

❒ First Angle :

$\dashrightarrow \sf First\: Angle =\: x$

$\dashrightarrow \sf\bold{\red{First\: Angle =\: 85^{\circ}}}$

❒ Other Angle :

$\dashrightarrow \sf Other\: Angle =\: x + 10^{\circ}$

$\dashrightarrow \sf Other\: Angle =\: 85^{\circ} + 10^{\circ}$

$\dashrightarrow \sf\bold{\red{Other\: Angle =\: 95^{\circ}}}$

$\sf\bold{\underline{\purple{\therefore\: The\: angles\: are\: 85^{\circ}\: and\: 95^{\circ}\: .}}}$