SOLUTION: Hi, I'm having a lot of trouble with problem, can I have some help please? "Rectangle ABCD has AB=6 and BC=3. Point M is chosen on side AB so that <AMD=<CMD. What is the degree

Algebra ->  Rectangles -> SOLUTION: Hi, I'm having a lot of trouble with problem, can I have some help please? "Rectangle ABCD has AB=6 and BC=3. Point M is chosen on side AB so that <AMD=<CMD. What is the degree      Log On


   

Question 1130943: Hi, I'm having a lot of trouble with problem, can I have some help please?
"Rectangle ABCD has AB=6 and BC=3. Point M is chosen on side AB so that Thank you!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Rectangle ABCD has AB=6 and BC=3.
Point M+is chosen on side AB so that < AMD = < CMD.
What is the degree measure of < AMD?"

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solution:
It is given that < AMD = < CMD. Since < AMD and < CMD are alternate interior angles and AB ||DC}, < AMD is congruent to < CMD --> < CMD is congruent to < CMD.
Use the Base Angle Theorem to show DC is congruent to MC.
We know that ABCD is a rectangle, so it follows that MC%7D+=+6%7D%7D.+%0D%0AWe+notice+that+%7B%7B%7B+BMC is a 30-60-90 triangle, and <+BMC+=+30°.
If we let x be the measure of < +AMD, then
2x%2B30=180
2x=180-30
2x=150
x=75