Question - Finding the Value of x in Parallel Line Segments with Given Angle Expressions
Solution:
\begin{align*}\text{Let } \angle ABC &= \angle BAC \text{ (alternate interior angles are equal because } AD \parallel BC) \\4x + 30^\circ &= 40^\circ \\4x &= 10^\circ \\x &= \frac{10^\circ}{4} \\x &= 2.5^\circ \\\end{align*}\text{Round to the nearest tenth: } x = 2.5^\circ
Tutor Solution:
The image shows a geometric figure with two parallel lines $$AD$$ and $$BC$$, and a transversal $$AB$$ cutting through them, forming two angles at point $$B$$. One angle is given as $$40^\circ$$, and the other is represented as $$(4x + 30)^\circ$$.Since $$AD$$ and $$BC$$ are parallel lines, and $$AB$$ is a transversal, the angles formed on the same side of the transversal and inside the parallel lines are consecutive interior angles. According to the Consecutive Interior Angles Theorem, these angles are supplementary, which means their sum is $$180^\circ$$.We have one angle as $$40^\circ$$ and the other as $$(4x + 30)^\circ$$. We can set up the following equation to find the value of $$x$$:$$40^\circ + (4x + 30)^\circ = 180^\circ$$.Now, simplify and solve for $$x$$:\[ \begin{align*}4x + 70^\circ &= 180^\circ - 40^\circ, \\4x + 70^\circ &= 140^\circ, \\4x &= 140^\circ - 70^\circ, \\4x &= 70^\circ, \\x &= \frac{70^\circ}{4}, \\x &= 17.5^\circ.\end{align*} \]Therefore, the value of $$x$$ is $$17.5$$ to the nearest tenth.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com