Question

geometry (h) - 2, term1, term2
4 - 2: savvy adaptive practice
find the values of x and y.
x = (simplify your answer.)
y = (simplify your answer.)

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Since the angle marked \(x^{\circ}\) and the \(59^{\circ}\) angle are vertical angles, \(x = 59\).

Step2: Consider triangle BCD

Assume triangle \(BCD\) is isosceles (from the congruence marks on the sides). In an isosceles triangle, the base - angles are equal. Let's assume the base - angles of \(\triangle BCD\) are equal. The sum of the interior angles of a triangle is \(180^{\circ}\). Since one angle of \(\triangle BCD\) is \(x = 59^{\circ}\), and the other two base - angles are equal, we can find \(y\). Let the base - angles be \(y\). Then \(y=\frac{180 - 59}{2}=\frac{121}{2}=60.5\).

Answer:

\(x = 59\)
\(y=60.5\)