Corresponding angles are congruent, alternate interior angles are congruent, same side or consecutive interior angles are supplementary, alternate exterior angles are congruent… This question hasn't been answered yet Ask an expert. Consecutive interior angles are supplementary. So the given angles are congruent. Corollary 12-A-3 There can be at most one obtuse angle in triangle. So [5x + 60] +  = 180. This framework of two pairs of consecutive congruent sides, opposite angles congruent, and perpendicular diagonals is … Then x = 5. Then 5x = 50. Divide both sides by 10. Move +130 to the right side. Previous question Next question Transcribed Image Text from this Question. Parallel Lines. D) If consecutive Interior angles are supplementary, then lines are parallel. Alternate Interior Angles Theorem If two parallel lines are intersected by a transversal, then the alternate interior angles are congruent. 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.. Since they are complementary there are 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. Show transcribed image text. C) If lines are parallel, then consecutive interior angles are supplementary. The given angles are consecutive interior angles in parallel lines. Corollary 12-A-2 There can be at most one right angle in 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). So x = 5. 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. A) If lines are parallel, then alternate Interior angles are congruent. B) If alternate Interior angles are congruent, then lines are parallel. 13) Given that a//b, solve for x. Alternate interior angles are congruent. then each pair of consecutive interior angles is supplementary. 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°). +60 + 70 = +130. Formally, consecutive interior angles may be defined as two interior angles lying on the same side of the transversal cutting across two parallel lines. Question: In The Figure, 21 And 22 Are Congruent Consecutive Interior Angles Alternate Interior Angles Alternate Extorior Angles. 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 … Expert Answer . Home Geometry. If two lines in a plane are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. So are angles 3 and 5. Theorem 3-6 Consecutive Interior Angles Theorem

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