Question

1. garden plus llc is fencing a triangular garden (pictured below) for mr. gold. part a: determine the expression for the measure of angle y. part b: if m∠i = 33 and m∠y = 14d - 19, then determine the value of d.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle YKI\), we have \(m\angle Y + m\angle K+m\angle I=180^{\circ}\), where \(m\angle K = 67^{\circ}\) and \(m\angle I = w^{\circ}\). So, \(m\angle Y=180-(67 + w)=113 - w\).

Step2: Substitute known values for part B

We know that \(m\angle I = 33^{\circ}\), \(m\angle K = 67^{\circ}\), and \(m\angle Y=14d - 19\). Using the angle - sum property of a triangle \(m\angle Y+m\angle K + m\angle I=180^{\circ}\). Substitute the values: \((14d - 19)+67 + 33=180\).
First, simplify the left - hand side: \(14d-19 + 100=180\), which becomes \(14d+81 = 180\).
Then, subtract 81 from both sides: \(14d=180 - 81\), so \(14d=99\).
Finally, divide both sides by 14: \(d=\frac{99}{14}\).

Answer:

Part A: \(m\angle Y = 113 - w\)
Part B: \(d=\frac{99}{14}\)