Question

relationships continued > use the angle relationships shown in each diagram to complete the equations. 12 = 135 x = 13 4x + 12 = x = 14 = 67 x = 15 what term refers to the pair of labeled angles? are these angles congruent? if so, find the value of x. if not, explain why not.

Explanation:

Step1: Identify vertical - angle relationship

In problem 12, vertical angles are equal. So $3x = 135$.

Step2: Solve for x

Divide both sides of the equation $3x = 135$ by 3. So $x=\frac{135}{3}=45$.

Step3: Identify corresponding - angle relationship

In problem 13, corresponding angles are equal. So $4x + 12=112$.

Step4: Solve for x

Subtract 12 from both sides: $4x=112 - 12=100$. Then divide both sides by 4, $x = 25$.

Step5: Identify alternate - interior - angle relationship

In problem 14, alternate - interior angles are equal. So $5x+98 = 67$.

Step6: Solve for x

Subtract 98 from both sides: $5x=67 - 98=-31$. Then $x=-\frac{31}{5}=-6.2$.

Step7: Identify vertical - angle relationship for problem 15

The labeled angles $(10x - 19)^{\circ}$ and $(3x + 9)^{\circ}$ are vertical angles. Vertical angles are congruent. So $10x-19 = 3x + 9$.

Step8: Solve for x

Subtract 3x from both sides: $10x-3x-19=3x - 3x+9$, which gives $7x-19 = 9$. Add 19 to both sides: $7x=9 + 19=28$. Divide both sides by 7, $x = 4$.

Answer:

1. $3x$, $45$
2. $112$, $25$
3. $5x + 98$, $-6.2$
4. The term is vertical angles. They are congruent. $x = 4$