Question

find the value of x.
1)
2)
3)
4)
5)
6)
7)
8)
9)

Explanation:

Step1: Use vertical - angle property (1)

Vertical angles are equal. For the first problem where we have $61^{\circ}$ and $(7x)^{\circ}$, we set up the equation $7x = 61$. Then $x=\frac{61}{7}\approx8.71$.

Step1: Use supplementary - angle property (2)

Supplementary angles add up to $180^{\circ}$. Given an angle of $135^{\circ}$ and $(x - 4)^{\circ}$, we have the equation $135+(x - 4)=180$. Simplify it: $135+x-4 = 180$, then $x=180-(135 - 4)=49$.

Step1: Use supplementary - angle property (3)

Since $(2x + 1)^{\circ}$ and $141^{\circ}$ are supplementary, we set up the equation $(2x + 1)+141=180$. Combine like - terms: $2x+142 = 180$. Subtract 142 from both sides: $2x=180 - 142=38$. Divide by 2: $x = 19$.

Step1: Use corresponding - angle property (4)

Corresponding angles are equal. If we assume the angles $68^{\circ}$ and $(x + 4)^{\circ}$ are corresponding, then $x+4=68$, and $x=64$.

Step1: Use supplementary - angle property (5)

The angle of $120^{\circ}$ and $(5x)^{\circ}$ are supplementary. So, $120 + 5x=180$. Subtract 120 from both sides: $5x=180 - 120 = 60$. Divide by 5: $x = 12$.

Step1: Use exterior - angle property (6)

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. If the exterior angle is $(4x)^{\circ}$ and the non - adjacent interior angles are $24^{\circ}$ and some other angle, assuming a simple case of a linear pair and angle relationships, if we assume the angle adjacent to $(4x)^{\circ}$ is supplementary to it and related to the $24^{\circ}$ angle, we have $4x=180-(180 - 24)=24$, then $x = 6$.

Step1: Use corresponding - angle property (7)

If $42^{\circ}$ and $(x - 9)^{\circ}$ are corresponding angles, then $x-9=42$, and $x=51$.

Step1: Use vertical - angle property (8)

Since $107^{\circ}$ and $(3x + 2)^{\circ}$ are vertical angles, we set up the equation $3x+2=107$. Subtract 2 from both sides: $3x=105$. Divide by 3: $x = 35$.

Step1: Use supplementary - angle property (9)

Since $126^{\circ}$ and $(3x)^{\circ}$ are supplementary, we set up the equation $126+3x=180$. Subtract 126 from both sides: $3x=180 - 126 = 54$. Divide by 3: $x = 18$.

Answer:

1. $x=\frac{61}{7}\approx8.71$
2. $x = 49$
3. $x = 19$
4. $x = 64$
5. $x = 12$
6. $x = 6$
7. $x = 51$
8. $x = 35$
9. $x = 18$