SOLUTION: M and N are the midpoints of sides RS and RT of △RST, respectively. Given: RM = RN = 3x + 1 ST = 7x − 2 m∠R = 60° Find: x, RM, and ST

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Question 1193077: M and N are the midpoints of sides
RS and RT of △RST, respectively.
Given:
RM = RN = 3x + 1
ST = 7x − 2
m∠R = 60°
Find:
x, RM, and ST
Answer by MathLover1(20850) (Show Source):
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Given:

< °
Find: , , and
if you draw the triangle and label the sides you will see that the smaller triangle is an isosceles triangle because two of its sides are equal. So the base angles have to be .
we can find the missing angles because we have measure of angle and we know that sum of interior angles in a triangle is .
Measure of angle = measure of angle
you will see that all the three angles in triangle are each.
So it is an triangle.
Then the 3rd side is equal to the first two sides and .
so we now have
using triangle mid segment theorem, we know that the midsegment ( line connecting the midpoints of two sides of a triangle is midsegment) is parallel to and it’s length is half of the length of
or
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plug in the values

then