Question

unit 3 test
willhite_k geometry a_section 1_fall 25/26 / unit 3 - line relationships
given: ( ell parallel m ), cut by transversal ( t ); ( mangle 1 = 70^{circ} )
prove: ( mangle 6 = 110^{circ} )
statements

1. ( ell parallel m ), cut by transversal ( t ); ( mangle 1 = 70^{circ} )
2. ( angle 1 ) and ( angle 7 ) are supplementary angles.
3. ( mangle 1 + mangle 7 = 180^{circ} )
4. ( 70^{circ} + mangle 7 = 180^{circ} )
5. ( mangle 7 = 110^{circ} )
6. ( angle 7 ) and ( angle 6 ) are vertical angles.

7.

1. ( mangle 6 = mangle 7 )
2. ( mangle 6 = 110^{circ} )

reasons

1. given
2. same-side exterior ( angle ) s theorem

3.

1. substitution
2. subtraction property of equality
3. def. vert. ( angle ) s
4. vert. ( angle ) s theorem
5. def ( cong angle ) s

9.
a. corresponding angles postulate
b. substitution
c. ( mangle 6 = mangle 7 )
d. ( angle 6 cong angle 7 )
e. definition of supplementary angles

Explanation:

Step1: Find reason for statement 3

Since \(\angle1\) and \(\angle7\) are supplementary angles (statement 2), by the definition of supplementary angles, \(m\angle1 + m\angle7=180^{\circ}\).

Step2: Find statement 7

Since \(\angle7\) and \(\angle6\) are vertical angles (statement 6), by the Vertical Angles Theorem (\(\angle7\cong\angle6\)), the statement is \(\angle6\cong\angle7\).

Step3: Find reason for statement 9

Since \(m\angle6 = m\angle7\) (statement 8) and \(m\angle7 = 110^{\circ}\) (statement 5), by substitution, \(m\angle6=110^{\circ}\).

Answer:

1. e; 7. d; 9. b