Question

Given that m∠IHJ=(3a+6)∘ and m∠KHJ=(5a−18)∘, identify m∠IHJ.

The figure shows two triangles I H J and K H J with a common side H J. Side J I is perpendicular to side H I. Side J K is perpendicular to side H K. Sides J I and J K are congruent.

m∠IHJ = 24°
m∠IHJ = 84°
m∠IHJ = 12°
m∠IHJ = 42°

Answer 1

Well what would you think?

Answer 2

If sides JI and JK are congruent and both triangles have a right angle in it, what does that tell us about m∠IHJ and m∠KHJ?

Are they equal to each other?

Answer 3

Okay, I'll give it a shot.
Let's find a by setting the two equations equal to each other, since the angles are congruent.
3a+6 = 5a-18
Then we simply solve to find a:
(Subtract 6 from both sides)
3a=5a-24
(subtract 5a from both sides)
-2a=-24
(Divide both sides by -2)
a=12
Now we put a back into the equation for angle IHJ
3(12)+6
and we get (36+6 = 42)
42!
Check my math if I'm wrong please.