<PRE><B>Question 66377</B>
Isosceles Triangles
Triangles GHM and HJM are isosceles, with segment GH congruent to segment MH
and segment HJ congruent to segment MJ. Triangle KLM is equilateral, and the measure of angle HMK = 50. Find Each Measure.
YOU DID WELL TO EXPLAIN THE FIGURE.BUT STILL THERE IS A GAP
ON RELATIVE LOCATION OF K AND L WRT OTHER POINTS.LET ME ANSWER WHICH DOES
NOT NEED THIS INFORMATION FIRST 
1. Find the measure of angle KML.
60 DEG.SINCE KLM IS GIVEN AS EQUILATERAL.

2. Find the measure of angle HMG.
REQUIRES POSITION SKETCH...OR DATA
SEE 5 BELOW


3. Find the measure of angle GHM.
REQUIRES POSITION SKETCH..OR DATA
SEE 4 BELOW
4. If the measure of angle HJM = 145, find the measure of angle MHJ
IN TRIANGLE HJM,
HJ=MJ ...GIVEN
HENCE ANGLE HMJ=ANGLE HMJ=X
TOTAL OF ALL ANGLES = X+X+145=180
2X=35
X=17.5=ANGLE MHJ=ANGLE HMJ

5.If the measure of angle G = 67, find the measure of angle GHM. 
IN TRIANGLE HGM,
HG=MH ...GIVEN
HENCE ANGLE HGM=ANGLE GMH=67
TOTAL OF ALL ANGLES = 67+67+ANGLE GHM=180
ANGLE GHM = 180-67-67=46

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