Prove Line and Angle Theorems: CCSS.Math.Content.HSG-CO.C.9

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Geometry › Prove Line and Angle Theorems: CCSS.Math.Content.HSG-CO.C.9

Questions 1 - 10

1

What is the supplement of the complement of $62^{\circ}$ ?

$152^{\circ}$

$28^{\circ}$

$118^{\circ}$

$62^{\circ}$

$124^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $62^{\circ}$

The complement is

Since we are given an angle of $62^{\circ}$ we can substitute it for , and solve for .

$\90 = y + 62 \y = 28$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

$\180 = y + 28 \y = 152$

So the answer is $152^{\circ}$ .

2

What is the supplement of the complement of $18^{\circ}$ ?

$108^{\circ}$

$72^{\circ}$

$162^{\circ}$

$18^{\circ}$

$36^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $18^{\circ}$

The complement is

Since we are given an angle of $18^{\circ}$ we can substitute it for $\uptext{x}$ , and solve for $\uptext{y}$ .

$\90 = y + 18 \y = 72$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

$\180 = y + 72 \y = 108$

So the answer is $108^{\circ}$ .

3

What is the supplement of the complement of $4^{\circ}$ ?

$94^{\circ}$

$86^{\circ}$

$176^{\circ}$

$4^{\circ}$

$8^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $4^{\circ}$

The complement is

Since we are given an angle of $4^{\circ}$ we can substitute it for , and solve for .

$\90 = y + 4 \y = 86$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

$\180 = y + 86 \y = 94$

So the answer is $94^{\circ}$

4

What is the supplement of the complement of $48^{\circ}$ ?

$138^{\circ}$

$42^{\circ}$

$132^{\circ}$

$48^{\circ}$

$96^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $48^{\circ}$ .

The complement is

Since we are given an angle of $48^{\circ}$ we can substitute it for , and solve for .

$\90 = y + 48 \y = 42$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

$\180 = y + 42 \y = 138$

So the answer is $138^{\circ}$

5

What is the supplement of the complement of $76^{\circ}$ ?

$166^{\circ}$

$14^{\circ}$

$104^{\circ}$

$76^{\circ}$

$152^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $76^{\circ}$

The complement is

Since we are given an angle of $76^{\circ}$ we can substitute it for , and solve for .

$\90 = y + 76 \y = 14$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

$\180 = y + 14 \y = 166$

So the answer is $166^{\circ}$ .

6

What is the supplement of the complement of $45^{\circ}$ ?

$135^{\circ}$

$45^{\circ}$

$135^{\circ}$

$45^{\circ}$

$90^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $45^{\circ}$

The complement is

Since we are given an angle of $45^{\circ}$ we can substitute it for , and solve for .

$\90 = y + 45 \y = 45$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for

$\180 = y + 45 \y = 135$

So the answer is $135^{\circ}$ .

7

What is the supplement of the complement of $65^{\circ}$ ?

$155^{\circ}$

$25^{\circ}$

$115^{\circ}$

$65^{\circ}$

$130^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $65^{\circ}$

The complement is

Since we are given an angle of $65^{\circ}$ we can substitute it for , and solve for .

$\90 = y + 65 \y = 25$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for

$\180 = y + 25 \y = 155$

So the answer is $155^{\circ}$

8

What is the supplement of the complement of $71^{\circ}$ ?

$161^{\circ}$

$19^{\circ}$

$109^{\circ}$

$71^{\circ}$

$142^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $71^{\circ}$

The complement is

Since we are given an angle of $71^{\circ}$ we can substitute it for , and solve for .

$\90 = y + 71 \y = 19$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

$\180 = y + 19 \y = 161$

So the answer is $161^{\circ}$

9

What is the supplement of the complement of $66^{\circ}$ ?

$156^{\circ}$

$24^{\circ}$

$114^{\circ}$

$66^{\circ}$

$132^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $66^{\circ}$ .

The complement is

Since we are given an angle of $66^{\circ}$ we can substitute it for $\uptext{x}$ , and solve for $\uptext{y}$ .

$\90 = y + 66 \y = 24$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

$\180 = y + 24 \y = 156$

So the answer is $156^{\circ}$

10

What is the supplement of the complement of $40^{\circ}$ ?

$130^{\circ}$

$50^{\circ}$

$140^{\circ}$

$40^{\circ}$

$80^{\circ}$

Explanation

In order to solve this problem, we need to break down each word.

We need to first find the complement of $40^{\circ}$ .

The complement is

Since we are given an angle of $40^{\circ}$ we can substitute it for , and solve for .

$\90 = y + 40 \y = 50$

Now since we need to find the supplement of the answer, we just got.

The supplement is

Now we simply substitute the answer we just got for .

$\180 = y + 50 \y = 130$

So the answer is $130^{\circ}$

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