Question

problem 20: (first taught in lesson 30) △mno is equilateral. find x and y. after you enter your answer press go. x = y =

Explanation:

Step1: Find the value of \(x\)

Since \(\triangle MNO\) is equilateral, each angle is \(60^{\circ}\).
So, \(2x + 4x+2x=60\)
\(8x = 60\)
\(x=\frac{60}{8}= 7.5\)

Step2: Find the value of \(y\)

In an equilateral triangle, we can use the property of angles.
We know that one of the smaller triangles. Let's consider the triangle with angle \(y\).
The sum of angles in a triangle is \(180^{\circ}\). In the relevant small - triangle (using the side of the equilateral triangle), we have two sides equal (because of the equilateral triangle's side - splitting nature).
First, we know that \(2x = 2\times7.5 = 15^{\circ}\)
Using the angle - sum property of a triangle: \(y=180-(2x + 2x)\)
Substitute \(x = 7.5\), then \(2x=15\)
\(y=180-(15 + 15)\)
\(y = 150\)

Answer:

\(x = 7.5\), \(y=150\)