Question

HELP PLZ

In the figure, the line intersecting the top vertex is parallel to the base of the triangle.




Select from the drop-down menus to correctly complete the statements.


Angles 3, 4, and 5 form a straight angle, so the sum of the angles is ___ °. Because alternate interior angles are _____ when two parallel lines are cut by a transversal, you can substitute m∠4 for m∠1 , and m∠5 for m∠2 , making the sum of the measures of the interior angles equal to _____ °.

Answer 1

The sum of angles 3 , 4 and 5 is 180°

Alternate interior angles are equal

The sum of the measures of the interior angles equal to 180°

Explanation:

∵ ∠4 , ∠3 and ∠5 formed a straight angle

∵ The measure of the straight angle = 180°

∴ m∠4 + m∠3 + m∠5 = 180° ⇒ (1)

From the parallelism

m∠4 = m∠1 ⇒ alternate interior angles

m∠5 = m∠2 ⇒ alternate interior angles

By substituting in (1)

∴ m∠1 + m∠3 + m∠2 = 180°

∴ The sum of the measure of the interior angles in a triangle = 180°