Question

what are the values of x and y? r s 71° x y t x = ° y = ° submit

Explanation:

Step1: Identify triangle type

The triangle has two equal - side markings, so it is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the two equal angles be \(x\) and \(y\), and the third angle be 71°. So, \(x + y+71^{\circ}=180^{\circ}\). Since \(x = y\) (base - angles of isosceles triangle), we can rewrite it as \(2x+71^{\circ}=180^{\circ}\).

Step3: Solve for \(x\) and \(y\)

First, subtract 71° from both sides of the equation \(2x + 71^{\circ}=180^{\circ}\): \(2x=180^{\circ}-71^{\circ}=109^{\circ}\). Then divide both sides by 2: \(x = y=\frac{109^{\circ}}{2}=54.5^{\circ}\).

Answer:

\(x = 54.5\)
\(y = 54.5\)