Question

Given: ΔKLM, KL = LM, F ∈ LM m∠KFM = 75º m∠1=m∠2 Find: m∠K, m∠L and m∠M

Answer 1

The answer is m∠K=70º, m∠M=70º, and m∠L=40º.

Answer 2

Answer: m∠K = m∠M = 70° m∠L = 40°

Step-by-step explanation: ΔKLM is an isosceles triangle, as it has two sides of same length KL = LM, so the angles form with the base are also the same. The sum of all the angles in a triangle is 180°.

The point F in LM forms another triangle: ΔKFM. It is known that m∠KFM is 75° and that the line forming this new triangle cuts the m∠K in half, so:

m∠F + m∠M +
`(1)/(2)`.m∠K = 180

75 + x +
`(x)/(2)` = 180

x +
`(x)/(2)` = 180 - 75

`(x+2x)/(2)` = 105

3x = 210

x = 70

X is the angle in M, m∠M = 70°. Since m∠M = m∠K, m∠K = 70°

Now, to determine m∠L:

m∠M + m∠K + m∠L = 180

70 + 70 + m∠L = 180

m∠L = 180 - 140

m∠L = 40°

In conclusion, m∠M = 70°, m∠K = 70° and m∠L = 40°