Question

question
solve for x and then determine the measure of the exterior angle.

standard(s)
nc.7.g.5: use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step unknown angle in a figure.
other questions on this standard: 14
answer
a $x = 10; 60^\circ$
b $x = 25; 120^\circ$
c $x = 40; 180^\circ$
d $x = 85; 360^\circ$

Explanation:

Step1: Set up supplementary angle equation

The 60° angle and the exterior angle are supplementary, so their sum is 180°.
$$60 + (4x + 20) = 180$$

Step2: Simplify the left side

Combine like terms.
$$4x + 80 = 180$$

Step3: Isolate the term with x

Subtract 80 from both sides.
$$4x = 180 - 80$$
$$4x = 100$$

Step4: Solve for x

Divide both sides by 4.
$$x = \frac{100}{4} = 25$$

Step5: Calculate exterior angle

Substitute x=25 into $4x+20$.
$$4(25) + 20 = 100 + 20 = 120$$

Answer:

B. $x = 25; 120^\circ$