Answer:
- See the three answers below and the figures attached.
Explanation:
The figures with the three questions are attached.
1. Two lines meet at a point. Set up and solve an equation to find the value of [tex]x[/tex]
a) Identify the angle relationship(s).
- The two angles are vertical angles. Thus, they are equal.
b) Set up an equation that will yield the unknown value.
The angles are equal. You can ignore the symbol of degrees.
[tex]x+15=72[/tex]
c) Solve the equation for the unknown value.
Subtract 15 from both sides
[tex]x=72-15\\\\x=57[/tex]
d) Substitute the answer to determine the angle(s).
[tex]57\º+15\º=72\º[/tex]
2. Three lines meet at a point. Set up and solve an equation to find the value of [tex]a[/tex]. Is your answer reasonable? Explain how you know.
a) Identify the angle relationship(s).
The angle a is vertical with the angle in between 78º and 52º.
The three angles form a straight line.
b) Set up an equation that will yield the unknown value.
The three angles add up 180º. You can ignore the degree symbol:
[tex]78+a+52=180[/tex]
c) Solve the equation for the unknown value.
Subtract 78 and 52 from both sides and do the operations:
[tex]a=180-78-52\\\\a=50[/tex]
d) Substitute the answer to determine the angle(s).
[tex]a=50\º[/tex]
3. Two lines meet at a point that is also the endpoint of two rays. Set up and solve an equation to find the values of [tex]a[/tex] and [tex]b[/tex].
a) Identify the angle relationship(s).
- Angles a and 32º are complementary
- Angles a and b are complementary
b) Set up an equation that will yield the unknown value.
For a:
[tex]a+32=90[/tex]
For b:
[tex]a+b=90[/tex]
c) Solve the equation for the unknown value.
For a:
[tex]a=90-32\\\\a=58[/tex]
For b:
[tex]58+b=90\\\\b=90-58\\\\b=32[/tex]
d) Substitute the answer to determine the angle(s).
[tex]a=32\º\\\\b=32\º[/tex]
To check every answer you can use a protactor as suggested.
