# 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.

**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 .

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- B
- C
- D

**Q5: **

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

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- B
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- D

**Q6: **

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

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- 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.

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- D

**Q8: **

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

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- B
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- 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.

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- 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 .

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- 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 .

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- B
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- 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.

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**Q14: **

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

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- 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.

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**Q16: **

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

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**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 .

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- D

**Q18: **

Find the measure of the acute angle between and approximated to the nearest second.

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**Q19: **

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

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**Q20: **

Find the measure of the acute angle between and the -axis approximated to the nearest second.

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- 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.

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- 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 .

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**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.

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**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.

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- D