Question

In the figure below CEF is an equilateral triangle. Points B,C and E are collinear points A C F are collinear g =40 degrees and k=45 find angle h show all work

Answer 1

cef is equilateral so
l=m=n
l+m+n=180
so l=m=n=60
as l=i When two lines intersect, the opposite (X) angles are equal:
or i+j+k=180
i+j=135 eq1
j+k+l=180
j+l=135 eq 2
eq1-eq2
gives i=l
so i=60
g=40
g+h+i=180
h=80

Answer 2

∠h is 80°

Explanation:

Given: ΔCEF is an Equivalent Triangle

∠G = 40° and ∠k = 45°

To find: ∠h

we know that In equilateral triangle measure of all angles are 60°.

So, in ΔCEF

∠m = ∠n = ∠l = 60°

Vertically opposite angles are equal in measure

⇒ ∠i = ∠l = 60°

In ΔABC

∠g + ∠h + ∠i = 180° (Angle sum property)

40 + 60 + ∠h = 180

∠h = 180 - 100

∠h = 80°

Therefore, ∠h is 80°