Triangle Angle Theorems Answers

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

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 is shown with a line extending from the bottom left point

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 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 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 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.

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 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.

Which statements are always true regarding the diagram? Select three options.