Question

The measure of an angle is 30 degrees less than half the measure of its supplement. What is the measure of the angle?

A: 10
B: 40
C: 90
D: 140

Answer 1

supplementary angles add up to = 180

so,

x + y =180

but also, we are given that one of the angles is 30 less than half of the second which can also be written as

x = .5y - 30

we are looking for the value of x, so we can solve the first equation for y and then place it into the second equation

y = 180 - x

x = .5(180-x) -30

now we can solve for x

x = 90 - .5x -30

1.5x = 90 - 30

1.5x = 60

x = 40

so your answer should be

B) 40

hope this helps!

Answer 2

The concept of supplementary angles is :

Sum of supplementary angles =180 degrees

Now let us say one of the supplementary angle measures x degrees.

finding expression for second angle,

half the measure of x is 0.5x

30 degrees less means subtracting 30 so we have 0.5x-30

now the two angles are x and 0.5x-30

Adding the two will be equal to 180 , so forming an equation,

`x+0.5x-30 =180`

`1.5x-30 =180`

adding 30 on the right side,

`1.5x- =180+30`

`1.5x- =210`

dividing both sides by 1.5

x=210/1.5 = 140

So first angle is 140

our angle is 0.5x-30 which is 40 degrees

Answer is 40 degrees