Question

find the values of x and y
x =

y =

Explanation:

Step1: Find y using linear pair

A linear pair of angles sums to \(180^\circ\). So, \(y + 110^\circ = 180^\circ\). Solving for \(y\), we get \(y = 180^\circ - 110^\circ = 70^\circ\).

Step2: Find x using isosceles triangle

The triangle is isosceles (two equal sides, so two equal angles \(x\) and \(x\), and base angle \(y = 70^\circ\)). The sum of angles in a triangle is \(180^\circ\). So, \(x + x + y = 180^\circ\). Substituting \(y = 70^\circ\), we have \(2x + 70^\circ = 180^\circ\). Subtract \(70^\circ\): \(2x = 110^\circ\). Divide by 2: \(x = 55^\circ\).

Answer:

\(x = 55\), \(y = 70\)