One angle in a triangle is 20 degrees more than the smallest angle in the triangle, while the other angle is 22 degrees more tha
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Answer:
Step-by-step explanation:
Consider triangles AMP and ADC. In these triangles,
- angle A is the common angle, so
by reflexive property;
- angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.
Hence, triangles AMP and ADC are similar by AA similarity theorem.
Similar triangles have proportional corresponding sides, thus
so
Consider triangles ACB and PCN. In these triangles,
- angle C is the common angle, so
by reflexive property;
- angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.
Hence, triangles ACB and PCN are similar by AA similarity theorem.
Similar triangles have proportional corresponding sides, thus
so
