Question

review test chapter 1

1. if m∠tuv=(9x + 2), m∠tuw=(8x - 11), and m∠wuv=(4x - 14), find the value of x.
2. if m∠gef is ten less than four times m∠deg and m∠def = 145, find m∠deg and m∠gef
3. ∠e and ∠f are complementary. if m∠e=(8x - 29) and m∠f=(3x + 53), find x and m∠f.
4. if bd bisects ∠abc, m∠dbc = 84, and m∠abc=(9x - 3), find the value of x.
5. classify ∠1 and ∠2 using all relationships that apply.

a. adjacent
b. vertical
c. complementary
d. supplementary
e. linear pair

1. classify ∠1 and ∠2 using all relationships that apply.

a. adjacent
b. vertical
c. complementary
d. supplementary
e. linear pair

1. classify ∠1 and ∠2 using all relationships that apply.

a. adjacent
b. vertical
c. complementary
d. supplementary
e. linear pair

1. classify ∠1 and ∠2 using all relationships that apply.

a. adjacent
b. vertical
c. complementary
d. supplementary
e. linear pair

Explanation:

Step1: For question 9

Since $\angle TUV=\angle TUW+\angle WUV$, we substitute the given angle - measures. So, $(9x + 2)=(8x - 11)+(4x - 14)$.
First, simplify the right - hand side: $(8x - 11)+(4x - 14)=8x+4x-11 - 14=12x-25$.
Then we have the equation $9x + 2=12x-25$.
Subtract $9x$ from both sides: $2 = 12x-9x-25$, which simplifies to $2 = 3x-25$.
Add 25 to both sides: $2 + 25=3x$, so $27 = 3x$.
Divide both sides by 3: $x = 9$.

Step2: For question 10

Let $m\angle DEG=x$. Then $m\angle GEF = 4x-10$.
Since $\angle DEF=\angle DEG+\angle GEF$ and $m\angle DEF = 145$, we have the equation $x+(4x - 10)=145$.
Simplify the left - hand side: $x+4x-10=5x-10$.
So, $5x-10 = 145$.
Add 10 to both sides: $5x=145 + 10=155$.
Divide both sides by 5: $x = 31$.
So, $m\angle DEG = 31$ and $m\angle GEF=4\times31-10=124 - 10 = 114$.

Step3: For question 11

Since $\angle E$ and $\angle F$ are complementary, $m\angle E+m\angle F = 90$.
Substitute $m\angle E=(8x - 29)$ and $m\angle F=(3x + 53)$ into the equation: $(8x - 29)+(3x + 53)=90$.
Simplify the left - hand side: $8x+3x-29 + 53=11x + 24$.
So, $11x+24 = 90$.
Subtract 24 from both sides: $11x=90 - 24=66$.
Divide both sides by 11: $x = 6$.
Then $m\angle F=3\times6 + 53=18 + 53=71$.

Step4: For question 12

Since $\overrightarrow{BD}$ bisects $\angle ABC$, $m\angle ABC = 2m\angle DBC$.
Given $m\angle DBC = 84$ and $m\angle ABC=(9x - 3)$, we have the equation $9x-3=2\times84$.
Simplify the right - hand side: $9x-3 = 168$.
Add 3 to both sides: $9x=168 + 3=171$.
Divide both sides by 9: $x = 19$.

Step5: For question 13

$\angle1$ and $\angle2$ share a common vertex and a common side, and their non - common sides are opposite rays. So they are adjacent, supplementary, and form a linear pair.

Answer:

A, D, E

Step6: For question 14

$\angle1$ and $\angle2$ are opposite angles formed by the intersection of two lines. They are vertical angles.