Question

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223 test unit 2 parallel lines and angles show all work for full credit

1. fill in the blank. assume that all angles are right angles. 2 pts each

a.______ name a plane parallel to dabh.
b.______ name the segment parallel to bf, cg, and dh.
c.______ name the segment perpendicular to ad and dc.

1. given that m || n, solve for all of the numbered angles. 2 pts each

m∠1 =____ m∠2 =____
m∠3 =____ m∠4 =____
m∠5 =____ m∠6 =____
m∠7 =______
given that p || q, answer the following questions. 3 pts each

1. x =______
2. m∠abc =______
3. m∠dcb =______

Explanation:

Step1: Solve for angles in the first figure (problem 2)

• For \(m\angle1\):

Since \(m\parallel n\), and \(\angle1\) and \(\angle5\) are corresponding angles. \(\angle5\) and the given \(54^{\circ}\) angle are supplementary (\(\angle5 + 54^{\circ}=180^{\circ}\)), so \(\angle5 = 126^{\circ}\). Then \(m\angle1=m\angle5 = 126^{\circ}\) (corresponding angles).

• For \(m\angle2\):

\(\angle2\) and \(\angle5\) are alternate - interior angles. So \(m\angle2=m\angle5 = 126^{\circ}\) (alternate - interior angles).

• For \(m\angle3\):

\(\angle3\) and the \(54^{\circ}\) angle are vertical angles. So \(m\angle3 = 54^{\circ}\) (vertical angles).

• For \(m\angle4\):

\(\angle4\) and \(\angle3\) are supplementary. So \(m\angle4=180^{\circ}-m\angle3=126^{\circ}\).

• For \(m\angle6\):

\(\angle6\) and \(\angle3\) are alternate - interior angles. So \(m\angle6=m\angle3 = 54^{\circ}\).

• For \(m\angle7\):

\(\angle7\) and \(\angle1\) are vertical angles. So \(m\angle7=m\angle1 = 126^{\circ}\).

• For \(m\angle8\):

\(\angle8\) and \(\angle2\) are vertical angles. So \(m\angle8=m\angle2 = 126^{\circ}\).

Step2: Solve for \(x\) in the second figure (problem 3)

Since \(p\parallel q\), \((12x - 15)^{\circ}\) and \((9x+27)^{\circ}\) are alternate - exterior angles.
Set up the equation \(12x-15=9x + 27\).
Subtract \(9x\) from both sides: \(12x-9x-15=9x-9x + 27\), \(3x-15 = 27\).
Add \(15\) to both sides: \(3x-15 + 15=27+15\), \(3x=42\).
Divide both sides by \(3\): \(x = 14\).

Step3: Solve for \(m\angle ABC\) (problem 4)

Substitute \(x = 14\) into \(12x-15\). \(m\angle ABC=(12\times14 - 15)^{\circ}=(168-15)^{\circ}=153^{\circ}\).

Step4: Solve for \(m\angle DCB\) (problem 5)

Substitute \(x = 14\) into \(9x + 27\). \(m\angle DCB=(9\times14+27)^{\circ}=(126 + 27)^{\circ}=153^{\circ}\).

Answer:

• \(m\angle1 = 126^{\circ}\), \(m\angle2=126^{\circ}\), \(m\angle3 = 54^{\circ}\), \(m\angle4=126^{\circ}\), \(m\angle5 = 126^{\circ}\), \(m\angle6=54^{\circ}\), \(m\angle7 = 126^{\circ}\)
• \(x = 14\), \(m\angle ABC=153^{\circ}\), \(m\angle DCB=153^{\circ}\)