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juin [17]
3 years ago
6

Answer the Blanks:

Mathematics
1 answer:
vfiekz [6]3 years ago
6 0

Answer:

1. 90°

2. 90°

3. 40°

4. 45°

5. 45°

Step-by-step explanation:

<u>Given:</u> ΔABC,

CD⊥AB,

m∠A=50°,

m∠ACB=85°

<u>Solution:</u>

1. ∠ADC is a right ange, because CD⊥AB, so

m\angle ADC=90^{\circ}

2. ∠CDB is a right ange, because CD⊥AB, so

m\angle CDB=90^{\circ}

3. Consider triangle ACD. The sum of the measures of all interior angles is always 180°, so

m\angle A+m\angle ADC+m\angle ACD=180^{\circ}\\ \\50^{\circ}+90^{\circ}+m\angle ACD=180^{\circ}\\ \\m\angle ACD=180^{\circ}-50^{\circ}-90^{\circ}=40^{\circ}

4. By Angle Addition Postulate,

m\angle ACD+m\angle BCD=m\angle ACB\\ \\40^{\circ}+m\angle BCD=85^{\circ}\\ \\m\angle BCD=85^{\circ}-40^{\circ}=45^{\circ}

5. Consider triangle ABC. The sum of the measures of all interior angles is always 180°, so

m\angle A+m\angle ACB+m\angle B=180^{\circ}\\ \\50^{\circ}+85^{\circ}+m\angle B=180^{\circ}\\ \\m\angle B=180^{\circ}-50^{\circ}-85^{\circ}=45^{\circ}

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