Question

find the values of x and y...
*to solve for x - use the fact that all triangles add up to 180 degrees. add up all 3 angles inside the triangle and set it equal to 180!

Explanation:

Step1: Find the value of \(x\)

Use the triangle - angle sum property. The sum of the interior angles of a triangle is \(180^{\circ}\).
The three angles of the triangle are \((2x - 9)^{\circ}\), \((7x + 13)^{\circ}\), and \(41^{\circ}\).
So, \((2x-9)+(7x + 13)+41=180\).
First, simplify the left - hand side:

$$
LATEXBLOCK0
$$

Subtract \(45\) from both sides: \(9x=180 - 45=135\).
Divide both sides by \(9\): \(x=\frac{135}{9}=15\).

Step2: Find the value of \(y\)

Use the linear - pair property. The angle \((7x + 13)^{\circ}\) and \(y^{\circ}\) form a linear pair (they are supplementary, so their sum is \(180^{\circ}\)).
Since \(x = 15\), then \(7x+13=7\times15 + 13=105+13 = 118\).
Since \(y+(7x + 13)=180\), then \(y=180-(7x + 13)\).
Substitute \(x = 15\) into the equation: \(y=180-118 = 62\).

Answer:

\(x = 15\), \(y=62\)