91 points and will add answer as ! must show prosses though! match the angles to their measure. (show how you got the answers) answer choices: (10x + 3)° (173 - 15x)° (5x + 4)° (87 - 4x)° (4x + 3)° (86 - 5x)° angle hfg = angle bcf = angle fib =

Finding m<HFG:

Look at triangle HFG.

It has angles HFG, FGH, and GHF.

The sum of the measure of the angles of a triangle equals 180 deg.

m<FGH = 5x + 4

<GHF is a right angle, so it measures 90 deg.

m<HFG + m<FGH + m<GHF = 180

m<HFG + 5x + 4 + 90 = 180

m<HFG + 5x + 94 = 180

m<HFG = 180 - 94 - 5x

m<HFG = 86 - 5x

m<HFG = (86 - 5x)°

Finding m<BCF:

Quadrilateral IBCF is a rectangle because of the right angles shown.

BC is parallel to IH.

<A is congruent to <CBF because of corresponding angles.

m<A = m<CBF = 10x + 3

For triangle AGC,

m<A + m<G + m<C = 180

10x + 3 + 5x + 4 + m<C = 180

m<C + 15x + 7 = 180

m<C = 173 - 15x

m<BCF = (173 - 15x)°

Finding angle FIB:

BF and IH are parallel.

m<BFI = m<FIH = 4x + 3 by alternate interior angles.

Now look at triangle FBI.

m<IFB + m<FBI + m<FIB = 180

4x + 3 + 90 + m<FIB = 180

m<FIB + 4x + 93 = 180

m<FIB = 87 - 4x

m<FIB = (87 - 4x)°

Now look at <EFG. <EFG is an exterior angle of triangle FGI.

Theorem: The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles.

For exterior <EFG, the remote interior angles are <FIG and <FGI.

According to the theorem above,

m<FIG + m<FGI = m<EFG

Now we substitute the measure of each angle and solve for x.

4x + 3 + 5x + 4 = 9x + 7

the answer is 28

step-by-step explanation: