One angle of a triangle measures [tex]10degrees[/tex] more than the second. The measure of the third angle is twice the sum of the first two angles. What is the measure of each angle?

Respuesta :

Answer:

[tex]One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o[/tex]

Step-by-step explanation:

Let

x ----> the measure of one angle of the triangle

y ---> the measure of the second angle

z ----> the measure of the third angle

we know that

The sum of the measure of the interior angles in any triangle must be equal to 180 degrees

[tex]x+y+z=180^o[/tex] -----> equation A

One angle of a triangle measures  10 degrees more than the second

[tex]x=y+10[/tex] ----> equation B

The measure of the third angle is twice the sum of the first two angles

[tex]z=2(x+y)[/tex] ---> equation C

substitute equation B in equation C

[tex]z=2(y+10+y)[/tex]

[tex]z=4y+20[/tex] ----> equation D

substitute equation D and equation B in equation A

[tex](y+10)+y+(4y+20)=180^o[/tex]

solve for y

[tex]6y=180-30\\6y=150\\y=25^o[/tex]

Find the value of x

[tex]x=25+10=35^o[/tex]

Find the value of z

[tex]z=4(25)+20=120^o[/tex]

therefore

[tex]One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o[/tex]

ACCESS MORE
EDU ACCESS