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.
Accepted Solution
A:
Answer:∠ SVT = 18.5 degreesStep-by-step 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 [tex]\frac{1}{2}(360 - 143 \times 2) = 37[/tex] degrees each.
So, 2 × ∠ SVT = ∠ SVU = 37
⇒ ∠ SVT = 18.5 degrees (Answer)