Question

intro to algebra and geometric proof.
if free response this gets close to a lvl 4.
fill in the blank with choices ifs a lvl 3.
given: ( mangle nlm = 90 )
( mangle 1 = mangle 3 )
prove: ( mangle 2 + mangle 3 = 90 )
diagram with points l, m, n and angles 1, 2, 3
statements: blanks
reasons: blanks
choices (partial): substitution, segment addition postulate, angles go together, ( mangle 2 + mangle 1 = mangle nlm ), transitive property, ( mangle nlm = 90^circ ), ( mangle 1 = mangle 3 ), angle addition postulate, subtraction property of equality, given, start, ( mangle 2 + mangle 3 = 90 ), prove line, ( mangle 2 + mangle 1 = 90 ), ( angle nlm ) is a right angle

Explanation:

Step1: Identify Angle Addition

By Angle Addition Postulate, \( m\angle 1 + m\angle 2 = m\angle NLM \).

Step2: Substitute Given Angle

Given \( m\angle NLM = 90^\circ \), so \( m\angle 1 + m\angle 2 = 90^\circ \).

Step3: Substitute \( m\angle 1 = m\angle 3 \)

Using Substitution (since \( m\angle 1 = m\angle 3 \)), replace \( m\angle 1 \) with \( m\angle 3 \): \( m\angle 2 + m\angle 3 = 90^\circ \).

Answer:

\( m\angle 2 + m\angle 3 = 90 \) is proven by Angle Addition Postulate, given \( m\angle NLM = 90 \), and Substitution (using \( m\angle 1 = m\angle 3 \)).