Respuesta :

Answer:

x=15

y=5

Step-by-step explanation:

The small looking triangle has 3 angles that are congruent to each other. We know this because they all share that same single marker. That means each of those angles ate 60 degrees. That triangle is known as both a equilateral and equilangular. All that means is all of it's 3 sides are congruent and all of it's 3 angles are congruent.

So that angle that measures 8x forms a linear pair with the angle right next to it in the other triangle. All that means is that is supplementary to and adjacent to that angle that measures 60 degrees.

So we have 8x+60=180.

We need to solve this equation for x:

8x+60=180

Subtract 60 on both sides:

8x. =120

Divide both sides by 8

x. =120/8

x. =15

Now to find y.

The bigger looking triangle is an isosceles. We know this because its two base angles are congruent (they have the same double marker). This means 5y+1=26.

Solving:

5y+1=26

Subtracting 1 on both sides:

5y. =25

Dividing 5 on both sides:

y. =5

boffeemadrid

The values of [tex]x[/tex] and [tex]y[/tex] are required.

[tex]x=15,y=5[/tex]

In the figure

[tex]\angle BAD=\angle BDA[/tex]

This means the sides opposite to the angles will also be equal.

So, [tex]AB=BD=26[/tex]

In [tex]\Delta BDC[/tex] all angles are equal, so it is an equilateral triangle.

So, all angles are [tex]60^{\circ}[/tex]

[tex]\angle ABD+\angle DBC=180\\\Rightarrow 8x+60=180\\\Rightarrow x=\dfrac{180-60}{8}\\\Rightarrow x=15[/tex]

All sides are equal in [tex]\Delta BDC[/tex]

[tex]26=5y+1\\\Rightarrow y=\dfrac{26-1}{5}\\\Rightarrow y=5[/tex]

Learn more:

https://brainly.com/question/19829657?referrer=searchResults

Ver imagen boffeemadrid

Otras preguntas