Question

measurement of one angle of a complimentary angle is 10° more than another angle,then what will be the measurement of both the angles?​

Answer 1

Answer :-

• The measure of both the angles of a complementary angle are 40° and 50°.

Step-by-step explanation:

To Find :-

• Th measure of both angles

Solution:

Given that,

• The measurement of one angle of a complementary angle is 10° more than another angle.

Assumption:

• Let us assume the one complementary angle as (x)° and the other which is 10° more than other as (x+10)°,

As we know that,

• Sum of complementary angles = 90°

Therefore,

• (x)° + (x+10)° = 90°

By evaluating,

⟹ ( x ) + ( x + 10 ) = 90

⟹ x + x + 10 = 90

⟹ 2x + 10 = 90

⟹ 2x = 90 - 10

⟹ 2x = 80

⟹ x = 80/2

⟹ x = 40

Therefore, The value of x is 40.

Hence, The measure of both the angles are :-

The angle which we assumed as (x)°

• ( x )° = 40°

The angle which we assumed as (x+10)°

• ( x + 10 )° = ( 40 + 10 )° = 50°

Hence, The measure of both the angles of a complementary angle are 40° and 50°.

Answer 2

Given:-

One angle is 10°more than another angle

Find:-

The measurement of both angles.

Solution:-

Let the smaller angle be x

And bigger angle be x+10°

We know that the measure of complementary angle is 90°

∴x+x+10°=90°

2x=90°-10°

2x=80°

x=80°/2

∴x=40°

Small angle=40°

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The angle is x

∴x+10

Put the value of x

∴40°+10°=50°

Other angle =50°

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Verification

• Measure of complementary angle is 90°
• We will add both the given numbers if the sum of both is 90°Then the answer is correct.

∴40°+50°=90°

Hence verified ✔️

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Hence the measure of both complementary angle is 40° and 50°