Question

Triangle RSU is an equilateral triangle. RT bisects US. Find x and y. (y+12)°

Answer 1

Answer:

x= 4

y = 6

Step-by-step explanation:

Given:

RSU is equilateral triangle

RT bisects US

To Find:

x and y

Solution:

Step 1: Finding the value of x

In an equilateral triangle,

All the sides are equal

Since RT bisects US

US =  3x+3x

Also RU  =  4x+8

Then ,

we know that

RU = US

$4x+8 = 3x+3x$

$4x+8 = 6x$

$4x+ 8 -6x = 0$

$-2x+8 = 0$

$-2x = -8$

$x = \frac{-8}{-2}$

$x = 4$

Step 2: Finding the value of y

In an equilateral triangle,

All the angles are equal  to 60 degrees

Then $\angle URS = 30^{\circ}$

But RT bisects US

Then

$\angle URS = \angle URT +\angle TRS = 60^{\circ}$

where

$\angle URT and \angle RTS$ are equal

So

$\angle RTS = 30^{\circ}$

In the figure

$30^{\circ} = 5y^{\circ}$

$y^{\circ}= \frac{30^{\circ}}{5}$

$y^{\circ} = 6$