Question

In the diagram, line CE is parallel to segment AB. Vertex D of triangle ABC lies on line CE.

Shawn says that mz2+ m24+ m25 = 180°. Which angle relationships explain why Shawn
must be correct? Choose all that apply.

A. m<1 = m<5
B. m<3= m<4
C. m<1 + m<5 = 180°
D. m<3 + m<4 = 180°
E m<1 + m<2 + m<3 = 180°

Answer 1

The angle relationships that explain why Shawn must be correct are:

A. angle 1 = angle 5

B. angle 3= angle 4

E angle 1 + angle 2 + angle 3 = 180⁰

Relationship between angles formed by parallel lines and transversal.

When a transversal intersects parallel lines, corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent, and consecutive interior angles are supplementary, forming key geometric relationships in parallel line systems.

The sum of angles in a triangle is always 180⁰

This fundamental property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

From the figure

Given

CE||AB

AD and BD are transversals

angle 1 = angle5(interior alternate angles) BD is transversal.

angle 3= angle4(interior alternate angles, AD is a transversal)

angle1 + angle2 + angle 3 = 180° (sum of angles in ∆ABD)