Question

the angles are supplementary and the larger is 58 degree more than the smaller

Answer 1

let smaller angle be x
larger angle = x+58
x+x+58 = 180
2x = 180-58
2x =122
x = 122/2
x=61

Answer 2

Answer:

Required angles are 61° and 119°.

Step-by-step explanation:

Given,Angles are supplementary.

So,Sum of two angles is 180°.

If x is a angle then supplementary angle of x will be $(180° - x)$.

By some examples,we can understand this concept easily.

1.Supplementary angle of 98° is

$(180° - 98°) = 82°$

2.Supplementary angle of 45° is

$(180° - 45°) = 135°$

3.Supplementary angle of 125° is

$(180° - 125°) = 55°$

4.Supplementary angle of 80° is

$(180° - 80°) = 100°$

Here given larger angle is 58 degree more than the smaller angle.

Let small angle be y

So, larger angle be y+58°

According to question,

$y + y + 58° = 180°$

We are separating variable and constant part,

$2y = 180° - 58° = 122°$

$y = \frac{122°}{2} = 61°$

Therefore, required angles are 61° and (61°+58°)=119°