Question

classwork activity #7 vertical angles & linear pair
name: banca n
date: september 16, 2025
a/b day: a day
period: 2nd

1. solve for the unknown value. (linear pair angles)

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, i.e., their sum is 180°.

Step2: First pair: $(4x + 2)^{\circ}$ and $(2x+22)^{\circ}$

Set up the equation: $(4x + 2)+(2x + 22)=180$.
Combine like - terms: $6x+24 = 180$.
Subtract 24 from both sides: $6x=180 - 24=156$.
Divide both sides by 6: $x=\frac{156}{6}=26$.

Step3: Second pair: $2x^{\circ}$ and $90^{\circ}$

Set up the equation: $2x+90 = 180$.
Subtract 90 from both sides: $2x=180 - 90 = 90$.
Divide both sides by 2: $x = 45$.

Step4: Third pair: $b^{\circ}$ and $114^{\circ}$

Set up the equation: $b + 114=180$.
Subtract 114 from both sides: $b=180 - 114 = 66$.

Step5: Fourth pair: $(6x + 2)^{\circ}$ and $(x + 3)^{\circ}$

Set up the equation: $(6x + 2)+(x + 3)=180$.
Combine like - terms: $7x+5 = 180$.
Subtract 5 from both sides: $7x=180 - 5 = 175$.
Divide both sides by 7: $x = 25$.

Step6: Fifth pair: $(4x + 9)^{\circ}$ and $95^{\circ}$

Set up the equation: $(4x + 9)+95=180$.
Combine like - terms: $4x+104 = 180$.
Subtract 104 from both sides: $4x=180 - 104 = 76$.
Divide both sides by 4: $x = 19$.

Step7: Sixth pair: $(17 + 2x)^{\circ}$ and $(8x + 3)^{\circ}$

Set up the equation: $(17 + 2x)+(8x + 3)=180$.
Combine like - terms: $10x+20 = 180$.
Subtract 20 from both sides: $10x=180 - 20 = 160$.
Divide both sides by 10: $x = 16$.

Answer:

First pair: $x = 26$; Second pair: $x = 45$; Third pair: $b = 66$; Fourth pair: $x = 25$; Fifth pair: $x = 19$; Sixth pair: $x = 16$