Question

11/7 - isosceles and equilateral practice
find the value of x and y.
11 12 13 14 15 16 17 18 19 20

Explanation:

Step1: Determine the type of triangle

Since one angle is \(60^{\circ}\) and the triangle is isosceles (two sides are equal), it is an equilateral triangle. In an equilateral triangle, all sides are equal and all angles are \(60^{\circ}\).
So, \(3x + 8=23\)

Step2: Solve for \(x\)

Subtract \(8\) from both sides of the equation \(3x + 8=23\):
\(3x=23 - 8\)
\(3x=15\)
Divide both sides by \(3\):
\(x=\frac{15}{3}=5\)

Step3: Solve for \(y\)

Since all angles in an equilateral triangle are \(60^{\circ}\), we have \(6y = 60\)
Divide both sides by \(6\):
\(y=\frac{60}{6}=10\)

Answer:

\(x = 5\)
\(y = 10\)