Question

question 17 (1 point)
find the values of x and y.

x=

y=

blank 1:

blank 2:

Explanation:

Step1: Use the property of trapezoid angles

In a trapezoid, consecutive angles between the non - parallel sides are supplementary. Also, the sum of interior angles of a quadrilateral is \(360^{\circ}\).
We know that \(8x + 4x=180\) (supplementary angles).

$$8x + 4x=180$$

$$12x = 180$$

$$x=\frac{180}{12}=15$$

Step2: Find the value of \(y\)

Substitute \(x = 15\) into the angle sum formula of the quadrilateral.
The sum of interior angles of a quadrilateral: \(90+5y + 8x+4x=360\)
Since \(x = 15\), then \(8x+4x=12x = 180\)
The equation becomes \(90+5y+180 = 360\)

$$5y+270=360$$

$$5y=360 - 270$$

$$5y=90$$

$$y=\frac{90}{5}=18$$

Answer:

Blank 1: \(15\)
Blank 2: \(18\)