Question

Given: m∠ELG = 124° Prove: x = 28 3 lines are shown. A line with points D, L, G intersects a line with points E, L, H at point L. Another line extends from point L to point F between angle E L G. Angle D L E is (2 x) degrees. Complete the steps in the two-column proof.

Answer 1

angle addition postulate

2x = 56

Explanation:

Answer 2

The completed two-column proof:

Statement Reason

∠ELG = 124° Given

∠FLG = 180° - ∠ELG = 56° Angle subtraction

∠FLG = ∠DLG Vertical angles

∠DLG = 2x° Given

2x° = 56° Transitive property of equality

x = 28° Solve for x

Therefore, x = 28°.

Linear pair: Angles that form a straight line are called linear pairs. The sum of the angles in a linear pair is 180 degrees.

Alternate interior angles: Alternate interior angles are pairs of non-adjacent angles on the inside of two parallel lines that are crossed by a transversal. Alternate interior angles are congruent.

Substitute: This means that we are replacing a term with an equivalent expression.

Subtract: This means that we are removing a term from both sides of an equation.

Divide both sides by 2: This means that we are dividing each term in the equation by 2.

Therefore, we have proven that x = 28.