Question

given the diagram and ( mparallel n ), determine the measure of each angle.
( mangle1=) (circ)
( mangle2=) (circ)
( mangle3=) (circ)
( mangle4=) (circ)
( mangle5=) (circ)
( mangle6=) (circ)
( mangle7=) (circ)
( mangle8=) (circ)
( mangle9=) (circ)
( mangle10=) (circ)
blank 1:
blank 2:
blank 3:
blank 4:
blank 5:

Explanation:

Step1: Vertical angles

Vertical angles are equal. So \(m\angle1 = 53^{\circ}\) (vertical angle with the \(53^{\circ}\) angle), \(m\angle3=53^{\circ}\) (vertical angle with \(\angle1\)), \(m\angle2 = 180^{\circ}- 53^{\circ}=127^{\circ}\) (linear - pair with \(\angle1\)), \(m\angle6 = 180^{\circ}-90^{\circ}-53^{\circ}=37^{\circ}\) (sum of angles in a right - triangle: \(90 + 53+\angle6=180\)), \(m\angle4 = 90^{\circ}\) (right - angle).

Step2: Parallel lines and transversals

Since \(m\parallel n\), alternate - interior angles. \(\angle7\) and \(\angle2\) are alternate - interior angles, so \(m\angle7 = 127^{\circ}\). \(\angle8\) and \(\angle6\) are alternate - interior angles, so \(m\angle8 = 37^{\circ}\). \(\angle9\) and \(\angle6\) are vertical angles, so \(m\angle9 = 37^{\circ}\). \(\angle10\) and \(\angle7\) are vertical angles, so \(m\angle10 = 127^{\circ}\). \(\angle5 = 90^{\circ}\) (right - angle).

Answer:

Blank 1: \(53\)
Blank 2: \(127\)
Blank 3: \(53\)
Blank 4: \(90\)
Blank 5: \(90\)
Blank 6: \(37\)
Blank 7: \(127\)
Blank 8: \(37\)
Blank 9: \(37\)
Blank 10: \(127\)