Answer :
The value of j + k = 80
To solve the problem, we need to find the sum of angles J AND K given the following conditions:
CEF is an equilateral triangle, so each angle inside the triangle is 60°
∠= 40°
∠k = 55°
- Points B , C and E are collinear, and points A , C and F are collinear.
Analyzing the angles:
Since CEF is equilateral, ( ∠ ECF = 60°).
( ∠ACF ) is on a straight line, ( ∠ACF + ∠ FCE = 180°).
( ∠ACF = 180° - 60° = 120°).
Now, using the triangle ( ABC ):
- ∠BAC = 180° - (g + j) .
- Since (∠= 40°), ∠ BAC
= 180° - (40° + j)
= 140° - j .
Now, using the triangle DEF:
( ∠ CEF = 60°) and ( k = 55°), ( ∠ DEF = 180° - (60° + 55°) = 65°).
In ABC, ( ∠ACB = j + g ), and we know ( ∠ g = 40°).
∠ABC = 180° - ( ∠BAC + ∠ACB) .
(∠ABC = 180° - (140° - j + j + 40°) = j
Now, the sum j + k
= 25° + 55°
= 80°.
Complete question
check attachment
The correct answer is 60 degrees for angle "l".
let's analyze the problem:
The angles g and k are given as 40 degrees and 45 degrees respectively.
The triangle CEF is equilateral, meaning all its angles are 60 degrees.
Given that i and l are opposite angles (alternate interior angles), and
since angle i = angle l, we can conclude that angle l is also 60 degrees.
So, the correct answer is 60 degrees for angle "l".
Question
In the figure below, CEF is an equilateral triangle. Points B, C and E are collinear; Points A, C and F are collinear; g = 40 degrees; and k = 45 degrees. Find angle l. Show all work.
