Question

what is the value of x?
a 15
b 25
c 45
d 75

Explanation:

Step1: Use property of parallel - lines and corresponding angles

Since the two horizontal lines are parallel, the angle corresponding to the $135^{\circ}$ angle and the angle $(3x)^{\circ}$ and the $105^{\circ}$ angle are related by the angle - sum property of a triangle formed by the non - parallel sides of the trapezoid - like figure. The angle corresponding to the $135^{\circ}$ angle is also $135^{\circ}$ (corresponding angles for parallel lines).

Step2: Apply angle - sum property of a triangle

In the triangle formed, the sum of interior angles of a triangle is $180^{\circ}$. Let's consider the angles in the triangle. One angle is $135^{\circ}- 105^{\circ}=30^{\circ}$, another is $(3x)^{\circ}$, and the third is $45^{\circ}$. So, $3x + 30+45 = 180$.

Step3: Solve the equation for $x$

First, simplify the left - hand side of the equation: $3x+75 = 180$. Then subtract 75 from both sides: $3x=180 - 75=105$. Divide both sides by 3: $x = 35$. But there is no such option. Let's consider another approach.
Since the two horizontal lines are parallel, the sum of the co - interior angles on the same side of the transversal is $180^{\circ}$.
The co - interior angle to the $135^{\circ}$ angle in the trapezoid - like figure is $45^{\circ}$. The co - interior angle to the $105^{\circ}$ angle and $(3x)^{\circ}$ should satisfy the property that the sum of co - interior angles between parallel lines is $180^{\circ}$.
We know that $105+(3x)=180$.
Subtract 105 from both sides: $3x=180 - 105 = 75$.
Divide both sides by 3: $x = 25$.

Answer:

B. 25