Question

11/7 - isosceles and equilateral practice
use the diagram to find the requested values:
what is the value of y?
what is the value of x?
what is the m∠p? degrees

Explanation:

Step1: Determine the type of triangle

Since one angle is \(60^{\circ}\) and the triangle has two equal - length sides (marked with tick - marks), it is an equilateral triangle. In an equilateral triangle, all sides are equal and all angles are \(60^{\circ}\).

Step2: Solve for \(x\)

Set \(2x = 12\) (because in an equilateral triangle, all sides are equal).

$$
LATEXBLOCK0
$$

Step3: Solve for \(y\)

Set \(4y=12\) (because all sides of an equilateral triangle are equal).

$$
LATEXBLOCK1
$$

Step4: Find \(m\angle P\)

In an equilateral triangle, all angles are \(60^{\circ}\), so \(m\angle P = 60^{\circ}\)

Answer:

The value of \(y\) is \(3\).
The value of \(x\) is \(6\).
\(m\angle P\) is \(60\) degrees.