∠CAT and ∠TAD are a linear pair, if M∠CAT = 2x-5 and M∠TAD = 5x+10, what is the measure of ∠CAT and ∠TAD? Draw a picture labelling the given information and show your work
Accepted Solution
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Answer:The answer to your question is: m∠CAT = 45; m∠TAD = 135Step-by-step explanation:Data∠CAT and ∠TAD are a linear pairm∠CAT = 2x-5m∠TAD = 5x+10m∠CAT = ? m∠TAD = ?ProcessThe sum of linear pairs angles equals 180°, so m∠CAT + m ∠TAD = 180° (2x - 5) + (5x + 10) = 180° 2x - 5 + 5x + 10 = 180Solve for x 7x + 5 = 180 7x = 180 - 5 7x = 175 x = 175 / 7 x = 25m∠CAT = 2(25) - 5 = 50 -5 = 45m∠TAD = 5(25) + 10 = 125 + 10 = 135