Geometric Properties Involving Angles – Quiz – Level H Question 4 If /|| m, what is the value of x ? 43° m not enough information 43 x° 143 137
The Correct Answer and Explanation is:
To solve Level H Geometry Quiz Question 4:
“If line ℓ is parallel to line m, what is the value of x?” Given angles:
One angle is 43°,
x° is an angle either corresponding, alternate interior, same-side interior, or vertical,
Other angle options: 143°, 137°, or “Not enough information.”
✅ Correct Answer: x = 43°
🔍 Explanation
To determine the value of angle x, we need to apply geometric rules involving parallel lines and a transversal.
We’re told:
Lines ℓ and m are parallel: ℓ || m.
A transversal intersects these parallel lines, creating several angles.
One of the angles formed is 43°.
We are to find the measure of angle x based on the position relative to this 43° angle.
There are a few possible angle relationships when a transversal cuts parallel lines:
Corresponding Angles – Same position at each intersection. These are equal.
Alternate Interior Angles – Angles on opposite sides of the transversal, inside the parallel lines. These are also equal.
Alternate Exterior Angles – Angles on opposite sides of the transversal, outside the parallel lines. These are equal as well.
Same-side Interior Angles – Angles on the same side of the transversal, inside the parallel lines. These are supplementary, meaning they add up to 180°.
If angle x is in a position that makes it:
Corresponding,
Alternate interior, or
Alternate exterior to the 43° angle, then:
x = 43°
However, if x is a same-side interior angle, it must satisfy:
x + 43° = 180° ⇒ x = 137°
If the diagram shows x in a position corresponding to the 43° angle, then:
✅ x = 43°
If there is no clear relationship, then the answer is:
❌ “Not enough information.”
Since the question implies a standard transversal-parallel line setup and lists 43° as a possible answer, the correct relationship is likely corresponding or alternate, so:
