Question

In ∆ABC, m∠BAC=4x+10,m∠ABC=12x-6,and m∠BCA=3x+5

Use the given information to find the value of x (1 point). Show your work (2 points)
Now that you know x, find the measure of each angle. Show your work (2 points each).
m∠BAC
m∠ABC
m∠BCA
Find the measure of angle 1 and angle 2 (2 points each)
m∠1
m∠2
Angle BAC and Angle FAC are examples of what type of angle pair? (1 point)
Angle BCE and Angle DCA are examples of what type of angle pair? (1 point)
Answer:

Answer 1

Try this option, note: only calculation is performed, the last two question are missed.

Explanation:

to calculate 'x':

the rule: m∠BAC+m∠ABC+m∠BCA=180°; if to substitute m∠BAC=4x+10,m∠ABC=12x-6,and m∠BCA=3x+5, then 4x+10+12x-6+3x+5=180°; ⇔ x=9.

to calculate m∠BAC; m∠ABC; m∠BCA:

m∠BAC=4x+10; ⇒ m∠BAC=36+10=46°;

m∠ABC=12x-6; ⇒ m∠ABC=108-6=102°;

and m∠BCA=3x+5; ⇒ m∠BCA=27+5=32°.

to calculate the angle 1 and 2:

the fule is: m∠1+m∠BAC=180° and m∠2+m∠ABC=180°.

Then m∠1=180-m∠BAC=180-46=134°;

m∠2=180-m∠ABC=180-102=78°.