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algol [13]
3 years ago
15

What is the measurement of QP? Please show all the work on how you got your answer

Mathematics
1 answer:
Brums [2.3K]3 years ago
5 0

Answer:

QP = 5

Step-by-step explanation:

QP is half of QS, and if QS = 10, then QP = 5

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a) \frac{1}{3}

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Step-by-step explanation:

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Answer:

m\angle B=54^{\circ}

m\angle BAD=36^{\circ}

m\angle CDA=90^{\circ}

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Step-by-step explanation:

Given:

\overline{AB}\cong \overline{AC},

\overline{AD} bisects angle BAC

m\angle C=54^{\circ}

Triangle ABC is isosceles triangle, because \overline{AB}\cong \overline{AC}. Angles adjacent to the base of isosceles triangle ABC are congruent.

Hence,

m\angle C=m\angle B=54^{\circ}

The sum of the measures of all interior angles is 180°, so,

m\angle B+m\angle C+m\angle BAC=180^{\circ}\\ \\m\angle BAC=180^{\circ}-2\cdot 54^{\circ}=72^{\circ}

Since \overline{AD} bisects angle BAC, angles BAD and CAD are congruent by definition of angle bisector. So,

m\angle BAD=m\angle CAD=\dfrac{1}{2}m\angle BAC=\dfrac{1}{2}\cdot 72^{\circ}=36^{\circ}

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m\angle CDA=90^{\circ}

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