QuestionAugust 25, 2025

8. If mangle ABC is one degree less than three times mangle ABD and mangle DBC=47^circ find each measure.

8. If mangle ABC is one degree less than three times mangle ABD and mangle DBC=47^circ find each measure.
8. If mangle ABC is one degree less than three times mangle ABD and mangle DBC=47^circ find each measure.

Solution
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Answer

m\angle ABD = 24^{\circ}, m\angle ABC = 71^{\circ} Explanation 1. Define Variables Let m\angle ABD = x. Then m\angle ABC = 3x - 1. 2. Use Angle Addition Postulate Since m\angle ABC = m\angle ABD + m\angle DBC, we have 3x - 1 = x + 47. 3. Solve for x Simplify the equation: 3x - x = 47 + 1 \Rightarrow 2x = 48 \Rightarrow x = 24. 4. Calculate m\angle ABC Substitute x = 24 into m\angle ABC = 3x - 1: m\angle ABC = 3(24) - 1 = 71.

Explanation

1. Define Variables<br /> Let $m\angle ABD = x$. Then $m\angle ABC = 3x - 1$.<br />2. Use Angle Addition Postulate<br /> Since $m\angle ABC = m\angle ABD + m\angle DBC$, we have $3x - 1 = x + 47$.<br />3. Solve for $x$<br /> Simplify the equation: $3x - x = 47 + 1 \Rightarrow 2x = 48 \Rightarrow x = 24$.<br />4. Calculate $m\angle ABC$<br /> Substitute $x = 24$ into $m\angle ABC = 3x - 1$: $m\angle ABC = 3(24) - 1 = 71$.
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