Question

In ΔKLM , KT bisects ∠LKM and KT = TM. If ∠LTK is 80°, find the value of ∠LMK and ∠KLM.

Answer 1

In ΔKTM,
KT = TM  ...(given)
Therefore, ∠TKM = ∠TMK   ....(i)
Now, ∠KTl = ∠TKM + ∠TMK
80 = ∠TKM + ∠TKM = 2∠TKM  ...(from (i))
∠TKM = 40°  = ∠TMK = ∠LMK ........(ii)
But ∠TKM = ∠TKL  ...(KT is the angle bisector)
Therefore, ∠TKL = 40°
In ΔKTL,
∠TKL +∠KTL + ∠KLT = 180°
40° + 80° + ∠KLT = 180°
∠KLT = 60° = ∠KLM
∠KLM = 60° and ∠LMK = 40°.