Question

The measures of two supplementary angles have a ratio of 2:4. What is the measure of the smaller angle?

Answer 1

The word supplementary means equal to 180 degrees. The ratio is 2:4, meaning that you have to set up the equation 2x+4x=180. Next, combine like terms which should get you 6x=180. After that, divide 6 on both sides of the equation which should leave you with x=30. The smaller angle is 2x, so substitute 30 making the smaller angle 2(30) which equals 60. 60 is the measure of the smaller angle.

Answer 2

Supplementary angles together evaluate to 180°. The measure of the smaller angle for the given context is $60^\circ$

What are supplementary angles?

Two angels whose sum is 180° are called supplementary angles.

What is ratio of two quantities?

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b or  $\dfrac{a}{b}$

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

$a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3$

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unit-less(no units) quantity.

For the given case, we are given that:
Ratio of measure of two supplementary angles is 2:4

That can be missing some factor(as its ratio,so figures are not guaranteed to be preserved as original ones), say the factor is $x$ such that:

First angle's measure = $2x^\circ$

and second angle's measure = $4x^\circ$

Then, as they're supplementary angles, thus, their sum evaluates to 180 degrees.

$2x + 4x = 180\\6x = 180\\\text{Dividing both the sides by 6}\\\\\dfrac{6x}{6} = \dfrac{180}{6}\\\\x = 30$

Therefore, the measure of the first angle is $2x^\circ = 60^\circ$

and the measure of the third angle is $4x^\circ = 120^\circ$

As smaller angle is first angle obviously, thus, the measure of the smaller angle for the given context is $60^\circ$

Learn more about supplementary angles here:

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