Question

modeling real life find the values of x and y in the diagram of the sports pennant.

x =

y =

Explanation:

Step1: Find the value of \( x \)

Since the triangle is isosceles (marked with equal - side indicators), the base - angles are equal.
In a triangle, the sum of interior angles is \( 180^{\circ} \). Let the two equal angles be \( x\) and \( x\), and the third angle is \( 79^{\circ}\).
So, \(x + x+79^{\circ}=180^{\circ}\), which simplifies to \(2x=180^{\circ}-79^{\circ}\), and \(2x = 101^{\circ}\), then \(x=\frac{101^{\circ}}{2}=50.5^{\circ}\).

Step2: Find the value of \( y \)

Use the exterior - angle theorem. The exterior angle \( y\) is equal to the difference between \( 180^{\circ}\) and the non - adjacent interior angle.
Another way is to use the property that \(y\) is the exterior angle of the isosceles triangle. The two equal interior angles are \(x = 50.5^{\circ}\).
We know that \(y=x+(x - 79^{\circ})\) (using the exterior - angle property: \(y = 180^{\circ}-2x\) is also valid).
First, \(y=180^{\circ}-2x\). Substitute \(x = 50.5^{\circ}\) into the formula: \(y=180^{\circ}-2\times50.5^{\circ}=180^{\circ}-101^{\circ}=79^{\circ}\).

Answer:

\(x = 50.5\), \(y = 79\)