Question

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 please!

Answer 1

x=56 and the exterior angle is 116

Explanation:

We will call the unknown angle in the triangle y. Angle y and the angle (2x +4) form a straight line so they make 180 degrees.

y + 2x+4 =180

Solve for y by subtracting 2x+4 from each side.

y + 2x+4 - (2x+4) =180 - (2x+4)

y = 180-2x-4

y = 176-2x

The three angles of a triangle add to 180 degrees

x+ y+ 60 = 180

x+ (176-2x)+60 = 180

Combine like terms

-x +236=180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply each side by -1

-1*-x = -56*-1

x=56

The exterior angle is 2x+4. Substitute x=56 into the equation.

2(56)+4

112+4

116

Answer 2

`x^(\circ)=56^(\circ);`

The exterior angle has measure
`116^(\circ).`

Explanation:

Angle QRP and angle with measure of (2x+4)° are supplementary, then

`m\angle QRP+(2x+4)^(\circ)=180^(\circ),\\ \\m\angle QRP=180^(\circ)-(2x+4)^(\circ).`

The sum of the measures of all interior angles of the triangle is equal to 180°, then

`m\angle PQR+m\angle QRP+m\angle RPQ=180^(\circ),\\ \\x^(\circ)+180^(\circ)-(2x+4)^(\circ)+60^(\circ)=180^(\circ),\\ \\x^(\circ)-2x^(\circ)=-60^(\circ)+4^(\circ),\\ \\-x^(\circ)=-56^(\circ),\\ \\x^(\circ)=56^(\circ).`

The exterior angle has measure

`(2\cdot 56+4)^(\circ)=116^(\circ).`