Question

math 1024: arithmetic of angular measurements - homework name
find \\( \angle k l p \\), if given that \\( \angle q l m \\) is \\( 36^{circ} \\)
find the measure of \\( \angle k f g \\), if given that \\( \angle e f j \\) is \\( 56^{circ} \\)
find the measure of the highlighted angle if \\( \angle j f t \\) is \\( 120^{circ} \\) (remember, a full circle is \\( 360^{circ} \\))

Explanation:

First Problem (Find \(\angle KLP\) given \(\angle QLM = 36^{\circ}\))

Step1: Use the property of a straight - line angle

A straight - line angle is \(180^{\circ}\). Let \(\angle KLP=x\), \(\angle PLQ = 75^{\circ}\), and \(\angle QLM=36^{\circ}\). We know that \(x + 75^{\circ}+36^{\circ}=180^{\circ}\) (since \(K\), \(L\), and \(M\) are collinear).

Step2: Solve for \(x\)

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Second Problem (Find \(\angle KFG\) given \(\angle EFJ = 56^{\circ}\))

Step1: Use the right - angle and straight - line angle properties

We know that \(\angle EFJ+\angle JFK+\angle KFG = 180^{\circ}\) and \(\angle JFK = 90^{\circ}\) (right - angle). Let \(\angle KFG=y\). Then \(56^{\circ}+90^{\circ}+y=180^{\circ}\)

Step2: Solve for \(y\)

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Third Problem (Find the highlighted angle given \(\angle JFT = 120^{\circ}\))

Step1: Use the full - circle angle property

A full - circle angle is \(360^{\circ}\). Let the highlighted angle be \(z\). Then \(z+\angle JFT=360^{\circ}\)

Step2: Solve for \(z\)

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Answer:

1. \(\angle KLP = 69^{\circ}\)
2. \(\angle KFG=34^{\circ}\)
3. The highlighted angle \(=240^{\circ}\)