Question

16 fill in the blank 2 points find the values of x and y. (2y + 5)° (5x - 17)° (3x - 11)° x = type your answer... y = type your answer...

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $5x - 17=3x - 11$.
$5x-3x=- 11 + 17$
$2x=6$
$x = 3$

Step2: Use the fact that the sum of angles in a right - angle

The angle $(2y + 5)^{\circ}$ and $(3x - 11)^{\circ}$ are complementary (since they form a right - angle, $90^{\circ}$). Substitute $x = 3$ into $(3x - 11)$: $3x-11=3\times3 - 11=-2$. Then, $2y+5+3x - 11 = 90$. Substitute $x = 3$ into the equation: $2y+5+3\times3 - 11=90$.
$2y+5 + 9-11=90$
$2y+3=90$
$2y=87$
$y = 43.5$

Answer:

$x = 3$
$y = 43.5$