Chapter 1.4, Problem 40PPS

To determine

To calculate the value of $\angle HBC$

Answer to Problem 40PPS

  $\angle HBC=61°$

Explanation of Solution

Given information:

  $\angle EBC=31a-2,\angle EBH=4a+45$

Formula used:

None

Calculation: since BH is an angle bisector

  $\angle EBH=\frac{1}{2}\angle EBC$

Substituting the values in the expression

  $4a+45=\frac{1}{2}\left(31a-2\right)$

Using cross multiplication method

  $8a+90=31a-2$

Subtracting ninety both sides

  $8a=31a-92$

Subtracting thirty one a by both sides

  $-23a=-92$

Dividing by minus twenty three both sides

  $a=4$

Now, put value of a in $\angle HBC$

  $4a+45=4\times 4+45$

Solving further

  $16+45$

The final answer is

  $61°$