Alternate interior angles are congruent. C) If lines are parallel, then consecutive interior angles are supplementary. Then x = 5. Theorem 3-6 Consecutive Interior Angles Theorem Show transcribed image text. +60 + 70 = +130. If consecutive interior angles are supplementary, then the lines are parallel As seen in the picture above there are consecutive interior angles which are supplementary( adds up to 180 degrees). This framework of two pairs of consecutive congruent sides, opposite angles congruent, and perpendicular diagonals is … Move +130 to the right side. Question: In The Figure, 21 And 22 Are Congruent Consecutive Interior Angles Alternate Interior Angles Alternate Extorior Angles. If two lines in a plane are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. B) If alternate Interior angles are congruent, then lines are parallel. 13) Given that a//b, solve for x. 62 = 8 x + 6 56 = 8 x 56 — 8 = 8 x — 8 x = 7 11. m ∠ 1 = 100 °, m ∠ 2 = 80 °, m ∠ 3 = 100 °; Because the 80 ° angle is a consecutive interior angle with both ∠ 1 and ∠ 3, they are supplementary by the Consecutive Interior Angles … Corollary 12-A-3 There can be at most one obtuse angle in triangle. So [5x + 60] + [70] = 180. Divide both sides by 10. Alternate Interior Angles Theorem If two parallel lines are intersected by a transversal, then the alternate interior angles are congruent. The given angles are consecutive interior angles in parallel lines. Theorem 3-5 Alternate Exterior Angles Theorem If two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent. So the given angles are congruent. Parallel Lines. Corollary 12-A-2 There can be at most one right angle in Home Geometry. So are angles 3 and 5. Previous question Next question Transcribed Image Text from this Question. Consecutive interior angles are supplementary. A) If lines are parallel, then alternate Interior angles are congruent. D) If consecutive Interior angles are supplementary, then lines are parallel. Corresponding angles are congruent, alternate interior angles are congruent, same side or consecutive interior angles are supplementary, alternate exterior angles are congruent… then each pair of consecutive interior angles is supplementary. This question hasn't been answered yet Ask an expert. Since they are complementary there are parallel lines. This means, that because the diagonals intersect at a 90-degree angle, we can use our knowledge of the Pythagorean Theorem to find the missing side lengths of a kite and then, in turn, find the perimeter of this special polygon.. Expert Answer . So x = 5. Formally, consecutive interior angles may be defined as two interior angles lying on the same side of the transversal cutting across two parallel lines. Consecutive Interior Angles Theorem The Theorem The Consecutive Interior Angles Theorem states that the two interior angles formed by a transversal line intersecting two parallel lines are supplementary (i.e: they sum up to 180°). Then 5x = 50. One angle is supplementary to both consecutive angles (same-side interior) One pair of opposite sides are congruent AND parallel So we’re going to put on our thinking caps, and use our detective skills, as we set out to prove (show) that a quadrilateral is a parallelogram.