Question

In the regular heptagon ABCDEFG, EH is the angle bisector of ∠E. Find ∠EHB

Answer 1

Answer:

Step-by-step explanation:

The formula for total angle of a polygon is

(n-2)x 180 = total angle for  a polygon

Given that ABCDEFG is a regular heptagon and EH is a angle bisector of angle E, then the total angle of the heptagon is

(7-2)x 180 = 900°

So each interior angle is  

900 ÷ 7 =128.571

(given heptagon is regular).

Since EH is a angle bisector

128.571 ÷2 = 64.2855

We have to find the angle EHB. For that we consider the pentagon HBCDE.

The total angle of the pentagon is given by .

=(n-2) x 180

= 5-2 x 180

=3 x 180

= 540°

Therefore angle EHB=The total angle of the pentagon -(each interior angle x 3 +∠ DEH and ∠FEH )

Therefore angle EHB = 540-(128.517+128.571+128.571+64.285)= 90.002 degree.

Ans= ∠EHB =90.002