Question

given the isosceles triangle below with sides and angles as marked, determine the value of x and y.
x=
y=

Explanation:

Step1: Identify triangle type

The triangle is isosceles and right - angled (one right angle, \(90^{\circ}\)). In an isosceles right - triangle, the two non - right angles are equal. Let the equal angles be \(x^{\circ}\) and \(9y^{\circ}\). So \(x = 9y\).

Step2: Use triangle angle sum

The sum of angles in a triangle is \(180^{\circ}\). For a right - triangle, one angle is \(90^{\circ}\), so \(x+9y + 90=180\). Since \(x = 9y\), substitute \(x\) in the equation: \(9y+9y + 90=180\).

Step3: Solve for y

Combine like terms: \(18y+90 = 180\). Subtract 90 from both sides: \(18y=180 - 90=90\). Divide both sides by 18: \(y=\frac{90}{18} = 5\).

Step4: Solve for x

Since \(x = 9y\) and \(y = 5\), then \(x=9\times5 = 45\).

Answer:

\(x = 45\)
\(y = 5\)