Question

section 2.4: arithmetic of angular measurements
find <eab 120 find <dab 70
find the missing angle if the total measure is 57° 15
15° 28
find the missing angles.

1. 2)
2. 4)
3. 6)

unit 2: angular measurements 2

Explanation:

Step1: Find \(\angle EAB\)

We know that \(\angle EAB=\angle EAD+\angle DAC+\angle CAB\). Given \(\angle EAD = 50^{\circ}\), \(\angle DAC=40^{\circ}\), and \(\angle CAB = 30^{\circ}\).

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Step2: Find \(\angle DAB\)

We know that \(\angle DAB=\angle DAC+\angle CAB\). Given \(\angle DAC = 40^{\circ}\) and \(\angle CAB=30^{\circ}\).

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Step3: Find the missing angle when total is \(57^{\circ}15'\) and one angle is \(15^{\circ}28'\)

We use the formula: Missing angle \(=\text{Total angle}-\text{Given angle}\).
First, convert \(57^{\circ}15'=56^{\circ}75'\) (since \(1^{\circ} = 60'\)).

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Step4: Solve for \(A\) in 1)

We know that \(A + 45^{\circ}=79^{\circ}\).

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Step5: Solve for \(A\) in 2)

We know that \(A + 80^{\circ}=135^{\circ}\).

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Step6: Solve for \(A\) in 3)

We know that \(61^{\circ}+A=170^{\circ}\).

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Step7: Solve for \(A\) in 4)

We know that \(A + 40^{\circ}=82^{\circ}\).

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Step8: Solve for \(A\) in 5)

We know that \(A+57^{\circ}=88^{\circ}\).

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Step9: Solve for \(A\) in 6)

We know that \(A + 30^{\circ}=73^{\circ}\).

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Answer:

\(\angle EAB = 120^{\circ}\), \(\angle DAB=70^{\circ}\), Missing angle \(=41^{\circ}47'\), 1) \(A = 34^{\circ}\), 2) \(A = 55^{\circ}\), 3) \(A = 109^{\circ}\), 4) \(A = 42^{\circ}\), 5) \(A = 31^{\circ}\), 6) \(A = 43^{\circ}\)