Question

modeling with mathematics the dimensions of a sports pennant are given in the diagram. find the values of x and y.

x=

y=

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the two equal sides correspond to the two equal angles. Here, the triangle is isosceles, so \(x = 15\) (the two equal sides).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the angles of the triangle be \(x^{\circ},x^{\circ},y^{\circ}\). Substitute \(x = 15\) into the angle - sum formula \(x + x+y=180\). So \(15+15 + y=180\), which simplifies to \(y=180-(15 + 15)=150\).

Answer:

\(x = 15\), \(y = 150\)