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 + [tex]\frac{1}{2}[/tex].m∠K = 180
75 + x + [tex]\frac{x}{2}[/tex] = 180
x + [tex]\frac{x}{2}[/tex] = 180 - 75
[tex]\frac{x+2x}{2}[/tex] = 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°
