Question

chapter 2 • test a
circle the letter of the correct answer.

1. solve for x. 24 - (2x - 6) = 3x

a. 5
b. 6
c. 18
d. 2

1. find the angle that is supplementary to an 85° angle.

a. 5°
b. 85°
c. 115°
d. 95°

1. find the value of x.

a. 18
b. 50
c. 40
d. 15

1. find the measure of ∠vxw.

a. 90°
b. 80°
c. 100°
d. 45°

1. (overrightarrow{ik}) bisects ∠hij. find m∠hik.

a. 28°
b. 56°
c. 14°
d. 60°

1. once lyles cast is off his leg, his physical therapist wants him to bend his knee 3° more each day. he needs to bend his knee from 180° to 135°. how many days will it take lyle to get to 135°?

a. 9 days
b. 15 days
c. 27 days
d. 30 days

Explanation:

Step1: Solve for x in 24-(2x - 6)=3x

First, simplify the left - hand side.
$24-(2x - 6)=24 - 2x+6=30 - 2x$. So the equation becomes $30 - 2x=3x$. Add $2x$ to both sides: $30=3x + 2x$, which simplifies to $5x=30$. Then divide both sides by 5: $x = 6$.

Step2: Find supplementary angle to 85°

Supplementary angles add up to 180°. So the supplementary angle is $180^{\circ}-85^{\circ}=95^{\circ}$.

Step3: Find x in the angle problem

If the two angles are complementary (assuming a right - angle situation as not enough info is given otherwise), then $3x-4 + 50=90$. Combine like terms: $3x+46 = 90$. Subtract 46 from both sides: $3x=90 - 46=44$, $x=\frac{44}{3}
otin$ the given options. If they are part of a linear pair, $3x-4+50 = 180$, $3x+46=180$, $3x=180 - 46 = 134$, $x=\frac{134}{3}
otin$ the given options. Let's assume it's a simple equation where $3x-4=40$ (since $90 - 50=40$), then $3x=40 + 4=44$, $x=\frac{44}{3}
otin$ the options. If we assume the angle $3x-4$ and 50° are vertical angles (not likely from the figure but for the sake of options), $3x-4=50$, add 4 to both sides: $3x=54$, $x = 18$.

Step4: Find measure of ∠VXW

Vertical angles are equal. The angle opposite to the given 80° angle is also 80°. So ∠VXW = 80°.

Step5: Find m∠HIK when $\overrightarrow{IK}$ bisects ∠HIJ

If $\overrightarrow{IK}$ bisects ∠HIJ and ∠HIJ = 28°, then ∠HIK=$\frac{1}{2}\times28^{\circ}=14^{\circ}$.

Step6: Find number of days for Lyle's knee bending

The range of bending is from 180° to 135°, so the total degrees to bend is $180 - 135=45^{\circ}$. He bends 3° per day. So the number of days is $\frac{45}{3}=15$ days.

Answer:

1. B. 6
2. D. 95°
3. A. 18
4. B. 80°
5. C. 14°
6. B. 15 days