Question

Find the measure of an angle which is 36° more than four-fifths of its supplement


explain step by step​

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

GiveN:

• There is a pair of supplementary angles.
• One of the angle is 36° more than four-fifths of its supplement.

To FinD:

• The measure of the angles?

Step-wise-Step Explanation:

Supplementary angles are the angles whose measures add upto 180°. Let the angles be x and y.

Then,

➛ x + y = 180° --------(1)

Now according to another condition given, one of them is 36° more than 4/5th of its supplement.

Then,

➛ x = 4y/5 + 36° --------(2)

Now putting the value of x in eq.(1),

➛ 4y/5 + 36° + y = 180°

➛ 9y/5 + 36° = 180°

➛ 9y/5 = 144°

➛ y = 144° × 5 / 9

➛ y = 80°

Then, x = 180° - 80° = 100°

Quick check:

= 4(80°)/5 + 36°

= 64° + 36°

= 100° (That is x)

Hence, Verified !!

Thus,

The required measures of the angles are:

$\huge{ \boxed{ \sf{ \pink{100 \degree \: and \: 80 \degree}}}}$

Answer 2

Answer:

$\huge \bf \: given \:$

Find the measure of an angle which is 36° more than four-fifths of its supplement

$\huge \bf \: to \: find$

the measure of an angle

$\huge \bf \: solution$

As we know that sum of supplementary angle is 180⁰.

Let the angle be x and y

After,

$x + y = 180 \degree$ Equation 1

Now according to the question one of them is more than four-fifth of its supplement

Then,

$x = \frac{4y}{5} + 36 \degree$

$\frac{4y}{5} + y + 36 = 180$

$\frac{9y}{36} = 180$

$\frac{9y}{36} = 180 - 36$

$\frac{9y}{36} = 144$

$y = 144 \times \frac{5}{9}$

$y = 80$

Now finding value of x

$x = 180 - y$

$x = 180 - 80$

$x = 100 \degree$

Thus the measure of angle are

$\huge {\fbox {\green {100 \degree \: and \: 80 \degree}}}$