7. which of the following statements is false?
not drawn to scale
a. ( mangle aeb = 60 )
b. ( angle bec ) and ( angle ced ) are adjacent angles.
c. ( mangle bec = 120 )
d. ( angle aed ) and ( angle bec ) are adjacent angles.
8. supplementary angles are two angles whose measures have sum _____.
complementary angles are two angles whose measures have sum _____.
a. 90; 180
b. 90; 45
c. 180; 360
d. 180; 90
9. two angles whose sides are opposite rays are called _____ angles. two coplanar angles with a common vertex, and no common interior points are called _____ angles.
a. vertical; adjacent
b. adjacent; vertical
c. vertical; supplementary
d. adjacent; complementary
10. how are the two angles related?
drawing not to scale
a. vertical
b. supplementary
c. complementary
d. adjacent
11. the complement of an angle is ( 25^circ ). what is the measure of the angle?
a. ( 75^circ )
b. ( 155^circ )
c. ( 65^circ )
d. ( 165^circ )
12. ( angle dfg ) and ( angle jkl ) are complementary angles. ( mangle dfg = x + 5 ), and ( mangle jkl = x - 9 ). find each angle.
a. ( angle dfg = 47 ), ( angle jkl = 53 )
b. ( angle dfg = 47 ), ( angle jkl = 43 )
c. ( angle dfg = 52 ), ( angle jkl = 48 )
d. ( angle dfg = 52 ), ( angle jkl = 38 )

Question

Accepted Answer

### Question 8
# Explanation:
## Step1: Recall definitions of supplementary and complementary angles.
Supplementary angles sum to $180^\circ$, complementary angles sum to $90^\circ$.
## Step2: Match with options.
So supplementary angles sum to $180$, complementary to $90$.
# Answer: d. 180; 90

### Question 9
# Explanation:
## Step1: Recall angle definitions.
Vertical angles have sides as opposite rays. Adjacent angles are coplanar, share a vertex, side, no common interior.
## Step2: Match terms.
First blank: vertical (sides opposite rays), second: adjacent (coplanar, common vertex, no common interior).
# Answer: a. vertical; adjacent

### Question 10
# Explanation:
## Step1: Calculate sum of angles.
$52^\circ + 128^\circ = 180^\circ$.
## Step2: Recall angle relation.
Angles summing to $180^\circ$ are supplementary.
# Answer: b. supplementary

### Question 11
# Explanation:
## Step1: Recall complementary angle formula.
If $A$ and $B$ are complementary, $A + B = 90^\circ$. Let the angle be $x$, its complement is $25^\circ$, so $x + 25^\circ = 90^\circ$.
## Step2: Solve for $x$.
$x = 90^\circ - 25^\circ = 65^\circ$.
# Answer: c. $65^\circ$

### Question 12
# Explanation:
## Step1: Use complementary angle sum.
Since $\angle DFG$ and $\angle JKL$ are complementary, $m\angle DFG + m\angle JKL = 90^\circ$. Substitute $m\angle DFG = x + 5$ and $m\angle JKL = x - 9$: $(x + 5) + (x - 9) = 90$.
## Step2: Solve for $x$.
Simplify: $2x - 4 = 90$ → $2x = 94$ → $x = 47$.
## Step3: Find angle measures.
$m\angle DFG = 47 + 5 = 52^\circ$, $m\angle JKL = 47 - 9 = 38^\circ$? Wait, no—wait, wait, let's check again. Wait, $x = 47$: $x + 5 = 52$, $x - 9 = 38$? But $52 + 38 = 90$, yes. Wait, but option d: $\angle DFG = 52$, $\angle JKL = 38$. Wait, but let's re - check the equation. $(x + 5)+(x - 9)=90$ → $2x - 4 = 90$ → $2x = 94$ → $x = 47$. Then $x + 5 = 52$, $x - 9 = 38$. So the answer is d? Wait, but let's check options:
a. $47$ and $53$: $47 + 53 = 100$ (not 90). b. $47$ and $43$: $47+43 = 90$, but $x + 5 = 47$ → $x = 42$, $x - 9 = 33$ (no). c. $52$ and $48$: $52 + 48 = 100$ (no). d. $52$ and $38$: $52+38 = 90$. So yes, d.
# Answer: d. $\angle DFG = 52$, $\angle JKL = 38$

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QUESTION IMAGE

Question

Explanation:

Question 8

Step1: Recall definitions of supplementary and complementary angles.

Step2: Match with options.

Step1: Recall angle definitions.

Step2: Match terms.

Step1: Calculate sum of angles.

Step2: Recall angle relation.

Answer:

Question 9