Question

Look at the picture. I need to find svt. The answer is 17 degrees but I don't know how to get that answer working it out.

Answer 1

∠ SVT = 18.5 degrees

Explanation:

See the given figure.

This is a diagram of a rhombus and the opposite angles of a rhombus are the same.

Now, ∠ VST = 5x + 23 and ∠ VUT = 8x - 49

And we have ∠ VST = ∠ VUT {Opposite angles}

So, 5x + 23 = 8x - 49

⇒ 3x = 23 + 49 = 72

⇒ x = 24

So, ∠ VST = 5x + 23 = 5 × 24 + 23 = 143

Hence, the other two opposite angles of the rhombus are
`(1)/(2)(360 - 143 * 2) = 37` degrees each.

So, 2 × ∠ SVT = ∠ SVU = 37

⇒ ∠ SVT = 18.5 degrees (Answer)