Question

1. identify the type of angles and their relationship. write the equation used to solve for x. then, find the value of x. put a box around your answer.
2. identify the type of angles and their relationship. write the equation used to solve for x. then, find the value of x. put a box around your answer.
3. identify the type of angles and their relationship. write the equation used to solve for x. then, find the value of x. put a box around your answer.

Explanation:

Step1: Analyze problem 2

The two angles $(x + 86)^{\circ}$ and $(2x+10)^{\circ}$ are congruent (assuming they are corresponding or vertical - angles which are equal in measure). Set up the equation $2x + 10=x + 86$.

Step2: Solve the equation for x

Subtract $x$ from both sides: $2x - x+10=x - x + 86$, which simplifies to $x+10 = 86$. Then subtract 10 from both sides: $x=86 - 10$.

Step3: Calculate the value of x

$x = 76$.

Step4: Analyze problem 3

The angles $(2x)^{\circ}$ and $(3x + 15)^{\circ}$ are supplementary (since they are adjacent - angles on a straight - line and their sum is $180^{\circ}$). Set up the equation $2x+(3x + 15)=180$.

Step5: Simplify the left - hand side of the equation

Combine like terms: $(2x+3x)+15 = 180$, so $5x+15 = 180$.

Step6: Solve for x

Subtract 15 from both sides: $5x+15 - 15=180 - 15$, which gives $5x = 165$. Then divide both sides by 5: $x=\frac{165}{5}=33$.

Step7: Analyze problem 4

The angles $(2x)^{\circ}$ and $98^{\circ}$ are supplementary (adjacent - angles on a straight - line). Set up the equation $2x+98 = 180$.

Step8: Solve for x

Subtract 98 from both sides: $2x=180 - 98$, so $2x = 82$. Then divide both sides by 2: $x = 41$.

Answer:

For problem 2: $x = 76$
For problem 3: $x = 33$
For problem 4: $x = 41$