Question

find the measure of an angle which is 36 degree more than four fifth of its supplement ​

Answer 1

Answer:

The angle is 100°

Step-by-step explanation:

Let the angle be x°

it's supplement be(180-x)°

ATQ

$x = \frac{4}{5} \times (180 - x) + 36 \\ x = (4 \times 36) - \frac{4x}{5} + 36 \\ x + \frac{4x}{5} = 36 \times 5 \\ \frac{9x}{5} = 36 \times 5 \\ x = 36 \times 5 \times \frac{5}{9} \\ x = 100$

Answer 2

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?

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°

= 4(80°)/5 + 36°

= 64° + 36°

= 100° (That is x)

Hence,

The required measures of the angles are 100° and 80°.