Triangle Angle Theorems Answers

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

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?

Triangle X Y Z is shown.

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.

A triangle with exterior angles is shown. A triangle sits on a line and forms 2 exterior angles on the left and right of the triangle of (2 h) degrees. The top interior angle of the triangle is 40 degrees.

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

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.

A triangle with exterior angles is shown. A horizontal line intersects with a diagonal line. Another line connects the horizontal line to the diagonal line to form a triangle. The exterior angle at the top left of the triangle is 130 degrees. The exterior angle at the top right of the triangle is x degrees. The exterior angle at the bottom of the triangle is 134 degrees.

Triangle A B C is shown with its exterior angles. Line B A extends through point D. Line A B extends through point E. Line A C extends through point F.

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.