Question

1. Identify the choice that best completes the statement or answers the question.

Two angles are complementary. The smaller angle is 35 deg. less than the larger angle. What is the measure of the larger angle?


A. 27.5 deg
B. 55 deg
C.62.5 deg
D. 125 deg

Answer 1

first, you should write it in mathematics language
there are two angles, let the smaller degree is x,
it's said that "The smaller angle is 35 deg. less than the larger angle"
then what is the larger angle (in term of x) ?

Answer 2

Well, when two angles are complementary, their measures add up to 90 degrees.

So, you have two angles that add up to 90 degrees. We'll name them x and y.

So the sum of angle x and angle y is 90 degrees because they are complementary. We can write this as:

x + y = 90

Now, we can't solve this as it is. However, we have one more piece of information, that the little angle is 35 degrees smaller than the bigger one.

We'll call x our little angle and y our big angle. We know that y is 35 degrees more than x. We can write this as:

x + 35 = y

Now, since we know what y is in terms of x, we can substitute it into our original equation:

x + (x + 35) = 90

Now, we'll just simplify and solve for x:

2x + 35 = 90
- 35 -35 Subtract 35 from both sides.
------------
2x = 55 Divide both sides by 2.
-- --
2 2

x = 55/2
Simplify.
x =27.5 degrees.

Now, we know the value of the little angle. But we need to find the value of the big angle, which is y.

But that's easy now that we know x.

Remember our first equation?

x + y = 90

Now, we can replace x with 27.5 since we know what x is.

27.5 + y = 90

And now we solve for y.

27.5 + y = 90
-27.5 -27.5 Subtract 27.5 from both sides.
---------------
y = 62.5

So y = 62.5 degrees, which is answer C.

Hope this helps! :)