the ratio the measurement of an angle to its complement is 1:2 . Find the measurement of the angle and its complement.

Question

Can you please help me solve this?

Answer 1

Hi Kelly

 

The angle and its complement will add to 90 degrees.

 

Since the ratio of the angle and its complement is 1:2, then we can say that x + 2x = 90 degrees

solve for x and you have the angle

 

multiple the angle by 2 and you have its complement.

Answer 2

Two angles are complementary if their measures add to 90 degrees.

 

Let x = measure of angle 1 and y = measure of angle 2.

 

Then:

 

x + y = 90

 

Now, we also know that the measure of angle 2 is twice that of angle 1 (the ratio of the measure of an angle to its complement is 1:2).

 

So:

 

y = 2x

 

Finally, substitute this value of y (2x) into the first equation (x + y = 90)

 

x + 2x = 90

 

=>

 

3x = 90

 

=>

 

x = 30 (measure of angle 1)

 

Then:

 

since y = 2x, y = 2 * 30 = 60 (measure of angle 2)

Answer 3

Kelly, if there are 1 part to 2, then there are 3 total parts. 90/3 = 30 degrees in one part.

 

Smaller angle then is 30 degrees and the larger is 2 parts or 60 degrees.

 

Hope this helps!