complementary and supplementary angles - practice worksheet
1. if angle a is 35°, what is the measure of its complementary angle?
2. if angle b is 112°, what is the measure of its supplementary angle?
3. two angles are complementary. if one is 64°, what is the other?
4. two angles are supplementary. one angle is 78°. find the other.
5. find the supplement of a 149° angle.
6. find the complement of a 27° angle.
7. if two angles are complementary and one is twice the other, what are the measures of both angles?
8. two angles are supplementary. one is three times the other. find both angles.
9. is a 91° angle complementary to a 89° angle? explain.
10. can two obtuse angles be supplementary? why or why not?
11. one angle is 40° more than its complement. find both angles.
12. one angle is 60° less than its supplement. find both angles.
13. if angle x and angle y are supplementary and angle x = 5x - 20, find x and y.
14. if angle a and angle b are complementary and angle a = 3a - 10, find a and b.
15. true or false: two right angles are always supplementary.

Question

Accepted Answer

# Explanation:
## Step1: Recall the definition of complementary angles
Complementary angles add up to $90^{\circ}$. Let the complementary angle of $A = 35^{\circ}$ be $x$. Then $x+35^{\circ}=90^{\circ}$.
## Step2: Solve for $x$
Subtract $35^{\circ}$ from both sides: $x = 90^{\circ}-35^{\circ}$.

# Answer:
$55^{\circ}$

# Explanation:
## Step1: Recall the definition of supplementary angles
Supplementary angles add up to $180^{\circ}$. Let the supplementary angle of $B = 112^{\circ}$ be $y$. Then $y + 112^{\circ}=180^{\circ}$.
## Step2: Solve for $y$
Subtract $112^{\circ}$ from both sides: $y=180^{\circ}-112^{\circ}$.

# Answer:
$68^{\circ}$

# Explanation:
## Step1: Use the property of complementary angles
Since two angles are complementary ($sum = 90^{\circ}$), if one angle $a = 64^{\circ}$, let the other angle be $b$. Then $a + b=90^{\circ}$.
## Step2: Solve for $b$
Substitute $a = 64^{\circ}$ into the equation: $b=90^{\circ}-64^{\circ}$.

# Answer:
$26^{\circ}$

# Explanation:
## Step1: Apply the property of supplementary angles
For two supplementary angles ($sum = 180^{\circ}$), if one angle $m = 78^{\circ}$, let the other angle be $n$. Then $m + n=180^{\circ}$.
## Step2: Solve for $n$
Substitute $m = 78^{\circ}$ into the equation: $n=180^{\circ}-78^{\circ}$.

# Answer:
$102^{\circ}$

# Explanation:
## Step1: Use the formula for supplementary angles
Let the supplement of $149^{\circ}$ be $s$. Since $s+149^{\circ}=180^{\circ}$.
## Step2: Solve for $s$
Subtract $149^{\circ}$ from both sides: $s = 180^{\circ}-149^{\circ}$.

# Answer:
$31^{\circ}$

# Explanation:
## Step1: Recall the formula for complementary angles
Let the complement of $27^{\circ}$ be $c$. Since $c + 27^{\circ}=90^{\circ}$.
## Step2: Solve for $c$
Subtract $27^{\circ}$ from both sides: $c=90^{\circ}-27^{\circ}$.

# Answer:
$63^{\circ}$

# Explanation:
## Step1: Set up equations
Let one angle be $x$, then the other angle is $2x$. Since they are complementary ($x+2x = 90^{\circ}$).
## Step2: Solve the equation
Combine like - terms: $3x=90^{\circ}$, then $x = 30^{\circ}$. The other angle $2x=60^{\circ}$.

# Answer:
$30^{\circ}$ and $60^{\circ}$

# Explanation:
## Step1: Establish equations
Let one angle be $p$, the other angle be $3p$. Since they are supplementary ($p + 3p=180^{\circ}$).
## Step2: Solve the equation
Combine like - terms: $4p=180^{\circ}$, then $p = 45^{\circ}$. The other angle $3p = 135^{\circ}$.

# Answer:
$45^{\circ}$ and $135^{\circ}$

# Explanation:
## Step1: Check the sum of angles
Calculate $91^{\circ}+89^{\circ}=180^{\circ}$. But complementary angles sum to $90^{\circ}$.

# Answer:
No, because $91^{\circ}+89^{\circ}=180^{\circ}$ (they are supplementary, not complementary as complementary angles sum to $90^{\circ}$).

# Explanation:
## Step1: Recall the definition of obtuse angles
An obtuse angle is greater than $90^{\circ}$. Let two obtuse angles be $m>90^{\circ}$ and $n>90^{\circ}$. Then $m + n>180^{\circ}$. But supplementary angles sum to $180^{\circ}$.

# Answer:
No. Because an obtuse angle $>90^{\circ}$, and if $A>90^{\circ}$ and $B>90^{\circ}$, then $A + B>180^{\circ}$ (supplementary angles sum to $180^{\circ}$).

# Explanation:
## Step1: Set up equations
Let one angle be $x$, its complement be $y$. We have $x=y + 40^{\circ}$ and $x + y=90^{\circ}$.
## Step2: Substitute and solve
Substitute $x=y + 40^{\circ}$ into $x + y=90^{\circ}$: $(y + 40^{\circ})+y=90^{\circ}$, $2y=50^{\circ}$, $y = 25^{\circ}$, then $x=65^{\circ}$.

# Answer:
$25^{\circ}$ and $65^{\circ}$

# Explanation:
## Step1: Set up equations
Let one angle be $u$, its supplement be $v$. We have $u=v - 60^{\circ}$ and $u + v=180^{\circ}$.
## Step2: Substitute and solve
Substitute $u=v - 60^{\circ}$ into $u + v=180^{\circ}$: $(v - 60^{\circ})+v=180^{\circ}$, $2v=240^{\circ}$, $v = 120^{\circ}$, then $u = 60^{\circ}$.

# Answer:
$60^{\circ}$ and $120^{\circ}$

# Explanation:
## Step1: Use the supplementary angle property
Since $x+y=180^{\circ}$ and $x = 5x-20$. First, solve $x = 5x-20$ for $x$: $4x=20$, $x = 5$. Then $y=180^{\circ}-x$.
## Step2: Calculate $y$
Substitute $x = 5$ into $y=180^{\circ}-x$: $y=175^{\circ}$.

# Answer:
$x = 5$, $y = 175^{\circ}$

# Explanation:
## Step1: Use the complementary angle property
Since $a + b=90^{\circ}$ and $a = 3a-10$. First, solve $a = 3a-10$ for $a$: $2a=10$, $a = 5$. Then $b=90^{\circ}-a$.
## Step2: Calculate $b$
Substitute $a = 5$ into $b=90^{\circ}-a$: $b = 85^{\circ}$.

# Answer:
$a = 5$, $b = 85^{\circ}$

# Explanation:
## Step1: Recall the measure of right angles
A right angle is $90^{\circ}$. Two right angles: $90^{\circ}+90^{\circ}=180^{\circ}$.

# Answer:
True. Because $90^{\circ}+90^{\circ}=180^{\circ}$ (supplementary angles sum to $180^{\circ}$).

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the definition of complementary angles

Step2: Solve for \(x\)

Step1: Recall the definition of supplementary angles

Step2: Solve for \(y\)

Step1: Use the property of complementary angles

Step2: Solve for \(b\)

Step1: Apply the property of supplementary angles

Step2: Solve for \(n\)

Answer: