Question

If EBC = 31a - 2 and EBH = 4a + 45 find HBC

Answer 1

HBC= 61°

Explanation:

31a-2=2(4a+45)

31a-2=8a+92-89

23a=92 divide both by 23

a=

Answer 2

The measure of angle HBC is m∠HBC=61°

Explanation:

In this problem we have that

The line BH bisects angle EBC,

see the attached figure to better understand the problem

then

m∠EBC=m∠EBH+m∠HBC

m∠EBH=m∠HBC

so

m∠EBC=2(m∠EBH)

substitute the given values and solve for a

`31a-2=2(4a+45)\\31a-2=8a+90\\31a-8a=92\\23a=92\\a=4`

Find the measure of angle EBH

m∠EBH=(4(4)+45)=61°

Remember that

m∠EBH=m∠HBC

therefore

The measure of angle HBC is m∠HBC=61°