Question

find the value of x and y in the isosceles trapezoid shown below.
(6x - 3)°
63°
y°
x=
y=
9
find the length of ef in the trapezoid shown

Explanation:

Step1: Solve for \( x \)

In an isosceles trapezoid, the base angles are equal. So, the angle \( 63^\circ \) and \( (6x - 3)^\circ \) are equal.
Set up the equation: \( 6x - 3 = 63 \)
Add 3 to both sides: \( 6x = 63 + 3 = 66 \)
Divide both sides by 6: \( x = \frac{66}{6} = 11 \)

Step2: Solve for \( y \)

In a trapezoid, consecutive angles between the bases are supplementary (their sum is \( 180^\circ \)).
So, \( y + 63 = 180 \)
Subtract 63 from both sides: \( y = 180 - 63 = 117 \)

Answer:

\( x = 11 \), \( y = 117 \)