Martha is training for a duathlon, which includes biking and running. She knows that yesterday she covered a total distance of o
ver 55.5 miles in more than than 4.5 hours of training. Martha runs at a speed of 6 mph and bikes at a rate of 15.5 mph.
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1.) You are correct.
2.) If ∠KQO = 58° and ∠AMI corresponds to it, then this means .
Substitute for x. ⇒
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3.) To solve this problem, try to think of triangle ΔQPK. All triangle angles have a sum of 180°. We already have 58. ∠HKQ is an exterior angle with a measure of 113°, so ∠PKQ is supplementary to it. 180 - 113 is 67. Now that we have two angle measures, the sum is 125, meaning that ∠KPQ is 55°. Because ∠MPL corresponds to it, this means it has the same measure of 55°.
4.) ∠KQO and ∠QOD are alternate interior angles, since they share the same transversal. If ∠KQO = 58°, then ∠QOD is also 58°.
5.) Angle ∠MPL is supplementary to ∠LPO. 180 - 55 = 125, so ∠LPO is 125°.