Question

name:
5.3 warm-up

1. if $\triangle mnp$ is an equilateral triangle, find the values of $x$ and $y$.

$n$ $(5y - 5)\degree$
$m$ $14$
$m$ $3x - 4$ $p$

Explanation:

Step1: Set side equal for x

In an equilateral triangle, all sides are equal. So we set the given sides equal:
$$3x - 4 = 14$$

Step2: Solve for x

Add 4 to both sides, then divide by 3:
$$3x = 14 + 4 = 18$$
$$x = \frac{18}{3} = 6$$

Step3: Set angle equal for y

In an equilateral triangle, all angles are $60^\circ$. Set the given angle equal to 60:
$$5y - 5 = 60$$

Step4: Solve for y

Add 5 to both sides, then divide by 5:
$$5y = 60 + 5 = 65$$
$$y = \frac{65}{5} = 13$$

Answer:

$x = 6$, $y = 13$