Triangle Angle Theorems Answers

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?

A triangle is shown with a line extending from the bottom left point

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.

Triangle Q R S is shown. Line R Q extends through point P. Angle Q S R is 35 degrees. Angle S R Q is 58 degrees. Exterior angle S Q P is x degrees.

Triangle X Y Z is shown.

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 R T S is sitting on a horizontal line. Line S R extends through point Q to form exterior angle T R Q. Angle R T S is (25 x) degrees. Angle T S R is (57 + x) degrees. Exterior angle T R Q is (45 x) 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 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.