Triangle Angle Theorems Answers

Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M.

Triangle Q R S is shown with exterior angles. Line R Q extends through point D. Line Q R extends through point E. Line Q S extends through point C.

Triangle X Y Z is shown. Line Z X is extended through point W to form exterior angle W X Y.

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.

A triangle is sitting on a horizontal line. The bottom left interior angle of the triangle is (9 + k) degrees. The exterior angle to the bottom left interior angle is (5 k minus 3) degrees.

Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.

Triangle A B F is shown. Line B F is extended through point G. Line F A is extended through point C. A line is drawn from point A to point D. A line is drawn from point F to point E.

A triangle has a bottom left angle of (x + 15) degrees and a bottom right angle of (x degrees). 1 parallel and horizontal line sits at the top point of the triangle. Another parallel and horizontal line sits at the base of the triangle. The exterior angle to the bottom right angle of the triangle is (4 x minus 20) degrees.

Given: Lines y and z are parallel, and ABC forms a triangle.Prove: m∠5 + m∠2 + m∠6 = 180° Statements Reasons1.ABC is a triangle1.given2.y ∥ z2.given3.∠1 ≅ ∠5; ∠3 ≅ ∠63.?4.m∠1 = m∠5; m∠3 = m∠64.def. ≅5.m∠1 + m∠2 + m∠3 = m∠LAM5.∠ addition postulate6.m∠1 + m∠2 + m∠3 = 180°6.def. straight angle7.m∠5 + m∠2 + m∠6 = 180°7.substitutionWhich could be the missing reason in Step 3?