Question

1. look at this diagram: if \\(\overleftrightarrow{hj}\\) and \\(\overleftrightarrow{km}\\) are parallel lines and \\(m\angle kln = 46^\circ\\), what is \\(m\angle hil\\)? \\(\square^\circ\\) 20. look at this diagram: if \\(\overleftrightarrow{pr}\\) and \\(\overleftrightarrow{su}\\) are parallel lines and \\(m\angle rqt = 125^\circ\\), what is \\(m\angle stq\\)? \\(\square^\circ\\)

Explanation:

Question 19

Step1: Identify angle relationship

Since \( \overleftrightarrow{HJ} \parallel \overleftrightarrow{KM} \) and \( \overleftrightarrow{GN} \) is a transversal, \( \angle HIL \) and \( \angle KLN \) are alternate interior angles. Alternate interior angles are equal when lines are parallel.

Step2: Determine \( m\angle HIL \)

Given \( m\angle KLN = 46^\circ \), by alternate interior angles theorem, \( m\angle HIL = m\angle KLN \).

Step1: Identify angle relationship

Since \( \overleftrightarrow{PR} \parallel \overleftrightarrow{SU} \) and \( \overleftrightarrow{VO} \) is a transversal, \( \angle STQ \) and \( \angle RQT \) are same - side interior angles. Same - side interior angles are supplementary, i.e., their sum is \( 180^\circ \).

Step2: Calculate \( m\angle STQ \)

We know that \( m\angle RQT = 125^\circ \) and \( m\angle STQ+m\angle RQT = 180^\circ \). So, \( m\angle STQ=180^\circ - m\angle RQT \).
Substitute \( m\angle RQT = 125^\circ \) into the formula: \( m\angle STQ = 180^\circ- 125^\circ=55^\circ \)

Answer:

\( 46 \)

Question 20