Question

if a kite has angle VST =(5x+23), angle VUT =(8x-49), angle V = 20, then what is the measurement of angle SVT?

Answer 1

To find the measurement of angle SVT, we first need to use the kite property that states the angles between the two congruent sides of a kite are congruent.

Given that angle V = 20 degrees, we can set up an equation using the angles we know:
Angle VST = 5x + 23
Angle VUT = 8x - 49

Since angle VST and VUT are congruent (since the sides SV and UT of the kite are congruent), we can set up an equation:

5x + 23 = 8x - 49

Rearranging the equation:
5x - 8x = -49 - 23
-3x = -72
x = 24

Now that we have found the value of x, we can find the measurement of angle SVT:
Angle VST = 5(24) + 23
Angle VST = 120 + 23
Angle VST = 143 degrees

Therefore, the measurement of angle SVT is 143 degrees.