The line joining 2 midpoints of two side of a triangle is parallel to the 3rd side and equal 1/2 its length
From the given figure
The line of length 34 is joining the midpoints of 2 sides of the triangle, then
It is = 1/2 x and parallel to it
[tex]\therefore34=\frac{1}{2}x[/tex]Multiply both sides by 2
[tex]\begin{gathered} \therefore34\times2=\frac{1}{2}x\times2 \\ \therefore68=x \end{gathered}[/tex]The value of x = 68
From the parallelism
The measure of the 3rd angle in the small triangle = y corresponding angles
[tex]\therefore y+41+76=180[/tex]Because the sum of angles of a triangle is 180 degrees
Add the like terms on the left side
[tex]\because y+117=180[/tex]Subtract 117 from both sides to find y
[tex]\begin{gathered} \because y+117-117=180-117 \\ \therefore y=63 \end{gathered}[/tex]The value of y is 63 degrees
