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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°

Respuesta :

meerkat18
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. 
SociometricStar

Answer:

126° and 54°

Step-by-step explanation:

Let the measurement of angles are x and y.

Then,

[tex]\frac{x}{y}=\frac{7}{3}\\\\x=\frac{7}{3}y...(i)[/tex]

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

Hence, we have

x + y = 180

From equation (i)

[tex]\frac{7}{3}y+y=180\\\\\frac{10}{3}y=180\\\\y=\frac{180\cdot3}{10}\\\\y=54[/tex]

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.

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