Question

PLEASE HELP

2. Quadrilateral EVWX is inscribed in a circle. Find the measure of angle X. (Remember to show formulas/equations and numbers in those formulas/equations to receive credit. Also, make sure to include units on your answer.)

Answer 1

`\hat{E} + \hat{V} + \hat{W} + \hat{X} = 360 \\ \Leftrightarrow \hat{V} = 360 - \hat{E} - \hat{W} - \hat{X} \\ \Leftrightarrow \hat{V} = 360 - 8x + 12 - 5x + 3 - 5x \\ \Leftrightarrow \hat{V} = - 18x + 375 \\ \hat{X} + \hat{V} = 180 \\ \Leftrightarrow - 18x + 375 + 5x = 180 \\ \Leftrightarrow - 13x = - 195 \\ \Leftrightarrow x = 15\\\Rightarrow \hat{X}=5 * 15=75°`

Answer 2

m∠x = 75°

Explanation:

Since sum of all angles in a quadrilateral EVWX = 360°

m∠E + m∠V + m∠W + m∠X = 360°

Since ∠X + ∠V = 180°

m∠E + m∠W = 180°

8x - 12 + 5x - 3 = 180

13x - 15 = 180

13x = 180 + 15 = 195

x = 195/13 = 15

Therefore ∠X = 5×15 = 75°