Question

1. find x. (11x - 8)° (4x - 7)° 10. explain why adjacent angles does not always provide enough information to solve for a missing angle measure. sketch an example. 11. error analysis ∠jkl and ∠xky are vertical angles. find x if m∠jkl=(7x + 2)° and m∠xky=(3x + 10)°. 7x + 2+3x + 10 = 180 10x + 12 = 180 10x = 168 x = 16.8

Explanation:

Step1: Identify angle - relationship for 8

The two given angles $(11x - 8)^{\circ}$ and $(4x - 7)^{\circ}$ are supplementary (a straight - line angle is 180°). So, we set up the equation $(11x - 8)+(4x - 7)=180$.
$$(11x - 8)+(4x - 7)=180$$

Step2: Simplify the left - hand side

Combine like terms: $11x+4x-8 - 7 = 180$, which simplifies to $15x-15 = 180$.
$$11x+4x-8 - 7=15x - 15$$

Step3: Solve for x

Add 15 to both sides of the equation: $15x-15 + 15=180 + 15$, so $15x=195$. Then divide both sides by 15: $x=\frac{195}{15}=13$.
$$15x=195\Rightarrow x = 13$$

For 11:

Step1: Identify the correct angle - relationship

Vertical angles are equal. So, we should set $m\angle{JKL}=m\angle{XKY}$, not their sum equal to 180°. The correct equation is $7x + 2=3x+10$.
$$7x + 2=3x+10$$

Step2: Solve for x

Subtract 3x from both sides: $7x-3x + 2=3x-3x + 10$, which gives $4x+2 = 10$. Then subtract 2 from both sides: $4x+2 - 2=10 - 2$, so $4x=8$. Divide both sides by 4: $x = 2$.
$$4x=8\Rightarrow x = 2$$

Answer:

For 8: $x = 13$
For 11: $x = 2$