1. what is the value of x? show your work to justify your answer. 2. what is the value of the exterior angle? show your work to justify your answer.

x=72 and the exterior angle is 154

Step-by-step explanation:

We will call the unknown angle in the triangle y.  Angle y and the angle (2x +10) form a straight line so they make 180 degrees.

y + 2x+10 =180

Solve for y by subtracting 2x+10 from each side.

y + 2x+10 - (2x+10) =180 - (2x+10)

y = 180-2x-10

y = 170-2x

The three angles of a triangle add to 180 degrees

x+ y+ 82 = 180

x+ (170-2x)+82 = 180

Combine like terms

-x +252=180

Subtract 252 from each side

-x+252-252 = 180-252

-x = -72

Multiply each side by -1

-1*-x = -72*-1

x=72

The exterior angle is 2x+10.  Substitute x=72 into the equation.

2(72)+10

144+10

154

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.