# Worksheet: Angle between Two Straight Lines in the Coordinate Plane

In this worksheet, we will practice finding the measure of an acute angle between two straight lines in the coordinate plane.

Q1:

Determine the measure of the acute angle between the straight line and the straight line passing through the points and to the nearest second.

• A
• B
• C
• D

Q2:

A line passing through makes an angle with the line , and . What is the equation of this line?

• A,
• B,
• C,
• D,

Q3:

Determine, to the nearest second, the measure of the acute angle between two straight lines having slopes of 5 and .

• A
• B
• C
• D

Q4:

Find, to the nearest second, the measure of the acute angle included between the straight line and the straight line whose slope is .

• A
• B
• C
• D

Q5:

Find the measure of the acute angle between the two straight lines whose equations are and to the nearest second.

• A
• B
• C
• D

Q6:

Determine the measure of the acute angle between the two straight lines and to the nearest second.

• A
• B
• C
• D

Q7:

Find the measure of the acute angle that lies between the straight line whose direction vector is , and the straight line whose equation is in degrees, minutes, and the nearest second.

• A
• B
• C
• D

Q8:

Find the measure of the acute angle between the following pair of straight lines: and .

• A
• B
• C
• D

Q9:

If the acute angle between the straight lines whose equations are and is , find all the possible values of .

• A,
• B, 1
• C, 7
• D, 16

Q10:

Let be the angle between two lines that pass through . If and the slopes of the lines are and , with , find the equations of these lines.

• A
• B
• C

Q11:

If is the measure of the acute angle between the two straight lines whose equations are and and , find all the possible values of .

• A
• B
• C
• D

Q12:

Determine the measure of the positive angle that the straight line makes with the positive direction of the -axis approximated to the nearest second, given that passes through points and .

• A
• B
• C
• D
• E

Q13:

Given that is a right triangle at , the equation of is , and the equation of is , find approximated to the nearest minute.

• A
• B
• C
• D

Q14:

Determine, to the nearest second, the measure of the positive angle that the straight line makes with the positive -axis.

• A
• B
• C
• D

Q15:

Let be the line on points and , and the perpendicular to that passes through the origin . What is the measure of the positive angle that makes with the positive -axis? Give your answer to the nearest second.

• A
• B
• C
• D

Q16:

Determine, to the nearest second, the measure of the positive angle that the straight line , makes with the positive -axis.

• A
• B
• C
• D

Q17:

Determine, to the nearest second, the measure of the positive angle made with the positive -axis by the perpendicular straight line to the straight line .

• A
• B
• C
• D

Q18:

Find the measure of the acute angle between and approximated to the nearest second. • A
• B
• C
• D

Q19:

Find, to the nearest second, the measure of the angle between the line and the positive -axis.

• A
• B
• C
• D

Q20:

Find the measure of the acute angle between and the -axis approximated to the nearest second. • A
• B
• C
• D

Q21:

If points , , and form a right-angled triangle at , find the value of , and then determine the measures of the other two angles to the nearest second.

• A, ,
• B, ,
• C, ,
• D, ,

Q22:

Find the measure of the acute angle included between the two straight line and whose equations are and , , respectively, in terms of degrees, minutes, and seconds, to the nearest second.

• A
• B
• C
• D

Q23:

Determine, to the nearest second, the measure of the positive angle that a straight line makes with the positive -axis while passing through the two points and .

• A
• B
• C
• D

Q24:

A line meets the -axis at 14 and the -axis at . Determine, to the nearest second, the measure of the positive angle that the line makes with the positive -axis.

• A
• B
• C
• D

Q25:

A line has slope 0.492. What is the measure of the angle that this line makes with the positive -axis? Give your answer to the nearest second.

• A
• B
• C
• D