In isosceles triangle PFA, mP is twelve degrees less than mF. P is one of the congruent angles.?

Question

What is the measure of each angle in triangle PFA?


I hope the question makes sense.. the m(variable) is where an angle sign would be approached. :)

Thanks.

Answer 1

So label mF as x degrees.
Then mP is x -12 and mA is also x - 12.
(if P is one of the congruent angles and it is smaller than F that means that A and P are congruent.)

So mF + mP + mA = 180 (all the angles of a triangle add to 180)
x + x-12 + x-12 = 180

Now solve for x. Once you have x, you will know mF, then subtract 12 and you will get mA and mP.

Hope this helps. :)

Answer 2

Three equations for three unknown variables:
(1) mP = mA
(2) mP + mA + mF = 180
(3) mF = mP + 12

Solve for mP first by substituting (1) and (3) into (2):
mP + mP + mP + 12 = 180
3*mP = 168
mP = 56

Putting that back into the other equations gives:
mA = 56
mF = 68

(did the arithmetic in my head, hope it is right.)

Answer 3

In triange PFA,

mF = mA

mP = mF - 12

Now, mP + mA + mF = 180

2mF + mF - 12 = 180

3mF = 192

mF = 64 degrees

mF = mA = 64 degrees

mP = 64 - 12 = 52 degrees

Answer 4

mP = mF - 12
mP = mA (since F is not congruent)

mP + mF + mA = 180
2mP + mF = 180

2(mF - 12) + mF = 180
2mF - 24 + mF = 180
3mF = 180 - 24
3mF = 156
mF = 156/3
mF = 52


Therefore
mF = 52
mP = 40
mA = 40

Answer 5

As stated, P must equal A because it's different than F and one of the equal angles. Therefore, as a few have concluded,

P = A = 56 deg and
F = 68 deg