Question

1. if ( mangle 8 = 23^circ ), find each measure. give your reasoning.

a. ( mangle 1 = )
b. ( mangle 2 = )
c. ( mangle 3 = )
d. ( mangle 4 = )
e. ( mangle 5 = )
f. ( mangle 6 = )
g. ( mangle 7 = )
this is a 2 - page document!
name:
unit 3: parallel & perpendicular lines
date:
per:
homework 2: parallel lines cut by a transversal

Explanation:

Step1: Identify Vertical Angles (∠8 and ∠2)

Vertical angles are equal. So \( m\angle2 = m\angle8 = 23^\circ \).

Step2: Identify Linear Pair (∠2 and ∠1)

Linear pair angles sum to \( 180^\circ \). So \( m\angle1 = 180^\circ - m\angle2 = 180^\circ - 23^\circ = 157^\circ \).

Step3: Identify Vertical Angles (∠1 and ∠3)

Vertical angles are equal. So \( m\angle3 = m\angle1 = 157^\circ \).

Step4: Identify Corresponding Angles (∠8 and ∠4)

Assuming parallel lines, corresponding angles are equal. So \( m\angle4 = m\angle8 = 23^\circ \).

Step5: Identify Vertical Angles (∠4 and ∠6)

Vertical angles are equal. So \( m\angle6 = m\angle4 = 23^\circ \).

Step6: Identify Linear Pair (∠8 and ∠7)

Linear pair angles sum to \( 180^\circ \). So \( m\angle7 = 180^\circ - m\angle8 = 180^\circ - 23^\circ = 157^\circ \).

Step7: Identify Vertical Angles (∠7 and ∠5)

Vertical angles are equal. So \( m\angle5 = m\angle7 = 157^\circ \).

Answer:

s:
a. \( m\angle1 = 157^\circ \)
b. \( m\angle2 = 23^\circ \)
c. \( m\angle3 = 157^\circ \)
d. \( m\angle4 = 23^\circ \)
e. \( m\angle5 = 157^\circ \)
f. \( m\angle6 = 23^\circ \)
g. \( m\angle7 = 157^\circ \)