Question

two supplementary angles differ by 50 degree find the measure of each angle

Answer 1

Here's the answer

Let the two angles be x and y.

We know tha
Supplementary angles measure 180°

Therefore,

x + y = 180° ... eq. (1)

Now,

According to the given condition,

x - y = 50° ... eq. (2)

Now,

Adding eq (1) and eq (2) ,

We get ,

$\: \: \: \: \: \: x + y = 180° \\ \: + \: \: x - y = 50 {}^{°} \\ - - - - - - - - - \\ \sf{2x = 230 {}^{°} }$

$\sf{x = 115°}$

Now,

As x - y = 50°,

Putting value of x in eq. (2),

115 - y = 50°

y = 115° - 50°

y = 65°

Thus,

We got values of x and y -

x = 115°

y = 65°

Thanks!!

Answer 2

Given:

Two supplementary angles differ by 50 degrees.

To Find:

The measure of each angle.

Solution:

1. Let the two unknown angles be x and y.

2. As the two angles are a supplement to each other, the sum of the angles made by them is equal to 180°.

=> x + y = 180. ( Assume as equation 1 ).

3. The difference between the two angles is 50°. Equaltinally it can be represented as,

=> x - y = 50. ( Assume as equation 2 ).

4. Add equations 1 and 2 for solving the values of x and y,

=> x + y + x - y = 180 + 50,

=> 2x = 230,

=> x = 115°.

5. Substitute the value of x in equation 1,

=> 115 + y = 180,

=> y = 180 - 115,

=> y = 65°.

Therefore, the measure of the two angles is 65° and 115°.