Question

The ratio of the measures of two supplementary angles is 7:3. Find the measures of the angles.

A. 126° and 54°
B. 72° and 18°
C. 159° and 21°
D. 69° and 21°

Answer 1

126° and 54°

Explanation:

Let the measurement of angles are x and y.

Then,

`(x)/(y)=(7)/(3)\\\\x=(7)/(3)y...(i)`

Now, the sum of two supplementary angles is 180 degrees.

Hence, we have

x + y = 180

From equation (i)

`(7)/(3)y+y=180\\\\(10)/(3)y=180\\\\y=(180\cdot3)/(10)\\\\y=54`

The second angle can be calculated as

x + 54 = 180

x = 180 - 54

x = 126

Therefore, the required angles are 126° and 54°

A is the correct option.

Answer 2

Supplementary angles are angles in which the total is equal to 180 degrees when summed. when the ratio of the angles is 7:3 we let x be angle 1 hence,

7x + 3x = 180
simplifying,
10 x =180
x = 18

Hence angle 1 is 126 degrees and angle 2 is 54 degrees. Answer is A.