Question

On the attached drawing what is the name for Angle LHJ? Obtuse, acute, complementary or right?

Answer 1

The correct answer is last option Right

Explanation:

From the figure we can see that,

AD ║ GJ and LE is the traversal.

And also given <ABE = 90°

Fro figure we get <ABE and <GHB are corresponding angles. Corresponding angles are equal.

Therefore <GHB = 90°

To find the <LHJ

From figure we can see that <LHJ and <GHB are vertically opposite angles.

Vertically opposite angles are equal.

Therefore <LHJ = <GHB = 90°

Answer 2

Answer: Right (Last option)

Explanation:

As you can see in the figure, the parallel lines AD and GJ are intersected by two lines.

The line EL intersects the parallel lines and there are two angles that are formed by this intersections which are located on the exterior of AD and GJ, but on opposite sides of EL, (these angles are called "Alternate exterior angles" and they are congruent), which are:

∠LHJ and ∠EBA

You can observe that the angle ∠EBA is indicated with a square. This means that the measure of that angle is 90° (Right angle).

Therefore, if ∠EBA=90°, then ∠LHJ =90°