Question

find the measure of each indicated angle.
1)
m\angle uwt =
2)
m\angle adc =
3)
m\angle pqs =
4)
m\angle efh =
5)
m\angle wxy =
6)
m\angle lok =
7)
m\angle xyw =
8)
m\angle qrt =
9)
m\angle cdf =

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles add up to \(180^{\circ}\).
For \(m\angle UWT\):
Since the given angle is \(53^{\circ}\), and \(\angle UWT\) and \(53^{\circ}\) are supplementary.
\(m\angle UWT=180 - 53\)

Step2: Calculate the value

\(m\angle UWT = 127^{\circ}\)

Step3: For \(m\angle ADC\)

Using the supplementary - angle property. Given \(170^{\circ}\), \(m\angle ADC=180 - 170\)

Step4: Calculate

\(m\angle ADC = 10^{\circ}\)

Step5: For \(m\angle PQS\)

First, note that the sum of angles around a point is \(360^{\circ}\).
\(m\angle PQS=360-(147 + 81)\)

Step6: Calculate

\(m\angle PQS=360 - 228=132^{\circ}\)

Step7: For \(m\angle EFH\)

Using supplementary - angle property. Given \(154^{\circ}\), \(m\angle EFH=180 - 154\)

Step8: Calculate

\(m\angle EFH = 26^{\circ}\)

Step9: For \(m\angle WXY\)

\(m\angle WXY=33 + 66\) (angle - addition postulate)

Step10: Calculate

\(m\angle WXY = 99^{\circ}\)

Step11: For \(m\angle LOK\)

Using supplementary - angle property. Given \(78^{\circ}\), \(m\angle LOK=180 - 78\)

Step12: Calculate

\(m\angle LOK = 102^{\circ}\)

Step13: For \(m\angle XYW\)

Using the property of vertical angles (vertical angles are equal). The angle vertical to \(112^{\circ}\) is equal, and \(m\angle XYW=180 - 112\) (supplementary to the vertical angle)

Step14: Calculate

\(m\angle XYW = 68^{\circ}\)

Step15: For \(m\angle QRT\)

Using supplementary - angle property. Given \(122^{\circ}\), \(m\angle QRT=180 - 122\)

Step16: Calculate

\(m\angle QRT = 58^{\circ}\)

Step17: For \(m\angle CDF\)

\(m\angle CDF=180-(140 + 37)\) (sum of angles on a straight line is \(180^{\circ}\))

Step18: Calculate

\(m\angle CDF=180 - 177 = 3^{\circ}\)

Answer:

1. \(127^{\circ}\)
2. \(10^{\circ}\)
3. \(132^{\circ}\)
4. \(26^{\circ}\)
5. \(99^{\circ}\)
6. \(102^{\circ}\)
7. \(68^{\circ}\)
8. \(58^{\circ}\)
9. \(3^{\circ}\)