Triangle ABC is congruent to triangle EDF, solve for x and y, and then find m<B.

Question

<A is on the left

<B is on the top

<C is on the right

<A= (6x+20) degrees

<C= (3y-2) degrees

Triangle EDF is upside down

<E is on the left

<F is on the right

<D is on the bottom

<E= (60-4y) degrees

<F= (8x-22) degrees

Answer 1

angle A = angle E, so 6x + 20 = 60 - 4y, gives you equation 3x + 2y = 20 ----- 1

angle C = angle F, so 3y - 2 = 8x - 22, gives you equation 8x - 3y = 20 -----2

multiply equation 1 by 3, multiply equation 2 by 2, add them together. You get,

25x = 100 so, x = 4. Plug in x = 4 in either equation 1 or 2, you get y = 4. Plugging in x = y = 4 we get,

angle A = 44 and angle C = 10. Angles in a triangle add up to 180, so angle B = 180 - (angle A + angle C) = 180 - (44 + 10) = 126.