Question

in the triangle, suppose that ( mangle q=(6x - 7)^{circ} ), ( mangle r=(2x - 2)^{circ} ), and ( mangle s = x^{circ} ).
(a) write an equation to find ( x ). make sure you use an \=\ sign in your answer.
equation:
(b) find the degree measure of each angle.
( mangle q=square^{circ} )
( mangle r=square^{circ} )
( mangle s=square^{circ} )

Explanation:

Step1: Sum angles to 180°

The sum of interior angles in a triangle is $180^\circ$. So add all angle measures:
$$(6x-7)+(2x-2)+x=180$$

Step2: Simplify left side

Combine like terms:
$$6x+2x+x-7-2=180$$
$$9x-9=180$$

Step3: Solve for x

Add 9 to both sides, then divide by 9:
$$9x=180+9$$
$$9x=189$$
$$x=\frac{189}{9}=21$$

Step4: Calculate each angle

Substitute $x=21$ into each angle expression:

• $m\angle Q = 6(21)-7 = 126-7$
• $m\angle R = 2(21)-2 = 42-2$
• $m\angle S = 21$

Answer:

(a) Equation:

$\boldsymbol{(6x-7)+(2x-2)+x=180}$

(b) Angle measures:

$m\angle Q = \boldsymbol{119}^\circ$
$m\angle R = \boldsymbol{40}^\circ$
$m\angle S = \boldsymbol{21}^\circ$