Question

I need help on a problem

Answer 1

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

`\therefore34=(1)/(2)x`

Multiply both sides by 2

`\begin{gathered} \therefore34*2=(1)/(2)x*2 \\ \therefore68=x \end{gathered}`

The value of x = 68

From the parallelism

The measure of the 3rd angle in the small triangle = y corresponding angles

`\therefore y+41+76=180`

Because the sum of angles of a triangle is 180 degrees

Add the like terms on the left side

`\because y+117=180`

Subtract 117 from both sides to find y

`\begin{gathered} \because y+117-117=180-117 \\ \therefore y=63 \end{gathered}`

The value of y is 63 degrees