Question

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find angles FAB and BAC

Answer 1

The measures are:

BAC = 180° - 13*6 + 3 = 105°

FAB = 13*6 - 3 = 75°

How to find the missing angles?

we know that the sum of the 3 interior angles of any triangle must be 180°, and we know that two adjacent angles always add up to 180°, then we know that:

A = 180° - 13x + 3

And then we can write the equation:

C + B + A = 180°

55 + 3x + 2 + 180 -13x - 3 = 180

55 + 3x + 2 - 13x + 3 = 0

60 - 10x = 0

60 = 10x

60/10 = x

6 = x

Then the measures are:

BAC = 180° - 13*6 + 3 = 105°

FAB = 13*6 - 3 = 75°

Answer 2

m<FAB = 75°

m<BAC = 105°

Explanation:

First, find the value of x.

(13x - 3)° = (3x + 2)° + 55° (exterior angle theorem of a ∆)

Solve for x

13x - 3 = 3x + 2 + 55

13x - 3 = 3x + 57

Collect like terms

13x - 3x = 57 + 3

10x = 60

Divide both sides by 10

x = 6

✔️m<FAB = 13x - 3

Plug in the value of x

m<FAB = 13(6) - 3 = 78 - 3

m<FAB = 75°

✔️m<BAC = 180 - m<FAB (angles on a straight line/supplementary angles)

m<BAC = 180 - 75 (substitution)

m<BAC = 105°