Question

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

Explanation:

Step1: Identify Triangle Type

The pennant is an isosceles triangle (two sides marked equal), so two angles are equal. The angle given is \(79^\circ\), and \(x^\circ\) is equal to \(79^\circ\) (base angles of isosceles triangle). So \(x = 79\).

Step2: Sum of Angles in Triangle

Sum of interior angles in a triangle is \(180^\circ\). Let the angles be \(x\), \(x\), and \(y\). So \(x + x + y = 180\). Substitute \(x = 79\): \(79 + 79 + y = 180\). Calculate \(79+79 = 158\). Then \(y = 180 - 158 = 22\).

Answer:

\(x = 79\), \(y = 22\)