In the diagram below, •WXZ is a right angle. If m•WXV is eleven more than three times m•WXY and m•YXV = 139°, find m•YXZ.

Answer 1

Here’s the way I drew it which was the only way that gave me whole number answers (which I’m assuming is what your teacher gave) - let me know if this isn’t the correct interpretation.

W = top

X = middle

Z = to the right of X

these 3 form a right angle

Y = diagonally up to the left connecting to X, left side of W

V = diagonally down to the right connecting to X, under Z

We are given that WXZ is a right angle = 90 degrees

We are also told that WXV is eleven more than 3 times WXY, and

YXV = 139

Ww are looking for YXZ

Let’s make an equation out of our information.

WXV is eleven more than 3 times WXY:

WXV

is =

eleven 11

more than +

3 times *3

WXY

WXV = 11 + 3*WXY

From our drawing (or my interpretation), we can see that WXY is actually a part of WXV. WXV is really WXY and YXV added together!

WXV = WXY + YXV

We have an expression for WXV that we just made that we can substitute into this equation. We also know the value for YXV = 139

11+ 3WXY = WXY + 139

We can solve this equation to find the measure of angle WXY

11+3WXY = WXY + 139 subtract 11 from both sides

3WXY = WXY + 128 subtract 1WXY from both sides

2WXY = 128 divide by 2 on both sides

Measure of WXY = 64

Now we can use this angle to find the measure of YXZ. We can look at the smaller angles that make up YXZ.

YXZ is made by WXY and WXZ

We know WXY = 64 and we were given WXZ right angle = 90

YXZ = WXY + WXZ

YXZ = 64 + 90

YXZ = 154 degrees

Hope this answers your question! If not please try to describe what the angles look like. :)