Question

In the diagram below of triangle I, J, KIJK, LL is the midpoint of start overline, I, K, end overline
IK
and MM is the midpoint of start overline, J, K, end overline
JK
. If mangle, K, J, I, equals, 104, minus, 8, x∠KJI=104−8x, and mangle, K, M, L, equals, 48, plus, 6, x∠KML=48+6x, what is the measure of angle, K, J, I∠KJI?

Answer 1

ML joins midpoints of IK and JK so ML is parallel to JI. Also MK lies along JK, so ∠KML and ∠KJI are corresponding angles and therefore equal.

Set them equal: 104 − 8x = 48 + 6x
104 − 48 = 14x
56 = 14x → x = 4

Then ∠KJI = 104 − 8(4) = 104 − 32 = 72° (checks with 48 + 6·4 = 72°).