Question

1. in the figure below, ba is perpendicular to line ( l ). what is the measure of ( angle abc )?

a. ( 53^circ )
b. ( 45^circ )
c. ( 37^circ )
d. ( 63^circ )

1. what does a linear pair form?

a. a right angle
b. an acute angle
c. a straight angle
d. an obtuse angle

Explanation:

Question 3

Step1: Identify right angle

Since \( BA \perp \text{Line } l \), \( \angle ABl = 90^\circ \).

Step2: Use vertical angles

The angle adjacent to \( 37^\circ \) (vertical angle) and \( \angle ABC \) sum to \( 90^\circ \). So \( \angle ABC = 90^\circ - 37^\circ = 53^\circ \).

A linear pair consists of two adjacent angles formed by intersecting lines, and their non - common sides form a straight line. A straight line measures \( 180^\circ \), which is a straight angle. A right angle is \( 90^\circ \), an acute angle is less than \( 90^\circ \), and an obtuse angle is greater than \( 90^\circ \) but less than \( 180^\circ \), so a linear pair forms a straight angle.

Answer:

A. \( 53^\circ \)

Question 4