Answer:
a.) [tex]x=12[/tex]
b.) [tex]A=50[/tex]
Step-by-step explanation:
a.) Remember: the sum of all angles in a triangle will always be 180°.
Make an equation in which all given angles add up to 180:
∠1+∠2+∠3=180
[tex](3x+14)+(7x-4)+50=180[/tex]
Solve the equation for the value of x. Remove the parentheses:
[tex]3x+14+7x-4+50=180[/tex]
Combine like terms:
[tex](3x+7x)+(14-4+50)=180\\\\10x+60=180[/tex]
Subtract 60 from both sides:
[tex]10x+60-60=180-60\\\\10x=120[/tex]
Divide both sides by 10:
[tex]\frac{10x}{10}=\frac{120}{10} \\\\x=12[/tex]
The value of x is 12.
b.) Insert the value of x into the given value of ∠A:
[tex]A=3x+14\\\\A=3(12)+14[/tex]
Simplify multiplication:
[tex]A=36+14[/tex]
Add:
[tex]A=50[/tex]
∠A is 50°.
:Done
Check Your Work:
To make sure the given values are true, solve for ∠B:
[tex]B=7(12)-4\\\\B=84-4\\\\B=80[/tex]
Now add all angle values to determine if they add up to 180°:
[tex]50+50+80=180\\\\100+80=180\\\\180=180[/tex]
Since 180 is equal to 180, the values are true.
