Answer:
x = 177/19 or ≈9.32
Step-by-step explanation:
To solve for x, first solve the exterior angle. Straight angles always equal 180° so in order to solve the exterior angle, add [(19x + 3) -180] to 19x+3
[(19x + 3) -180] + (19x+3) = 180 simplify by adding like terms
(19x - 177) + (19x + 3) =180
38x - 177 + 3 = 180
38x - 174 = 180 now solve for x, add 174 to 180
38x = 354 now divide 38 by 354
x = 177/19 or ≈ 9.32
To check x = 177/19, put it back into the equation [(19x + 3) -180] + (19x+3) = 180 {[19(177/19) + 3] -180} + [19(177/19)+3] = 180
It does equal 177/19
To solve for each angle, you would substitute x for 177/19
The bottom right angle: 6 (177/19) + 15 = 70 17/19 or ≈ 70.89
The top angle: 9 (177/19) + 16 = 99 16/19 or ≈ 99.84
To solve for the bottom left angle, you would add the other angles, then subtract the sum from 180 because all triangles equal 180°. This is the method I will use.
You could also substitute x for 177/19 in the equation 19x + 3, then subtract the product from 180.
The bottom left angle: (1347/19 + 1897/19) - 180 = 9 5/19 or ≈ 9.26
I hope this helps you, have a nice day
