a is parallel to b.Calculate the angles shown in the diagram.115115115111222333444555666777aaabbb

1, 3, 4, 6 = 65°; 2, 5, 7 = 115°

1, 3 = 65°; 2, 4, 6 = 115°; 5, 7 = 75°

Calculate 7 Angles with Parallel Lines: Given Angle 115°

Q: How do I know which angles are corresponding?

Corresponding angles are in the same relative position at each intersection. If one angle is at the top-right of the first intersection, its corresponding angle is at the top-right of the second intersection.

Q: Why are some angles 65° when the given angle is 115°?

Adjacent angles on a straight line are supplementary - they add to 180°. So if one angle is 115°, the angle next to it must be $ 180° - 115° = 65° $.

Q: What's the difference between vertical and corresponding angles?

Vertical angles are opposite each other at the same intersection point and are always equal. Corresponding angles are at different intersection points but in the same relative positions.

Q: Do I need to memorize all the angle relationship names?

Focus on understanding the patterns rather than memorizing names. Remember: opposite angles are equal, adjacent angles sum to 180°, and parallel lines create matching angles.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the angles

00:03 Adjacent angles are supplementary to 180

00:07 Therefore subtract the known angle from 180 to get the angle

00:28 (2,115) Vertical angles are equal

00:32 (3,60) Also a pair of vertical angles

00:48 (4,115) Corresponding angles between parallel lines are equal

00:55 (6,4) Vertical angles are equal

01:03 (5,65) Corresponding angles between parallel lines are equal

01:11 (5,7) Vertical angles are equal

01:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

a is parallel to b.

Calculate the angles shown in the diagram.

2

Step-by-step solution

Given that according to the definition, the vertex angles are equal to each other, it can be argued that:

$115=2$ Now we can calculate the second pair of vertex angles in the same circle:

$1=3$

Since the sum of a plane angle is 180 degrees, angle 1 and angle 3 are complementary to 180 degrees and equal to 65 degrees.

We now notice that between the parallel lines there are corresponding and equal angles, and they are:

$115=4$

Since angle 4 is opposite to angle 6, it is equal to it and also equal to 65 degrees.

Another pair of alternate angles are angle 1 and angle 5.

We have proven that: $1=3=65$

Therefore, angle 5 is also equal to 65 degrees.

Since angle 7 is opposite to angle 5, it is equal to it and also equal to 115 degrees.

That is:

$115=2=4=6$

$65=1=3=5=7$

3

Final Answer

1, 3 , 5, 7 = 65°; 2, 4 , 6 = 115°

Key Points to Remember

Essential concepts to master this topic

Corresponding Angles: Equal when formed by parallel lines and transversal
Supplementary Pairs: Adjacent angles sum to 180°, so 115° + angle = 180°
Verification: Check that vertical angles are equal and corresponding angles match ✓

Common Mistakes

Avoid these frequent errors

Confusing corresponding with alternate interior angles
Don't assume all angles between parallel lines are equal = wrong classifications! This mixes up which angles are actually equal to each other. Always identify the specific relationship first: corresponding angles are in the same relative position, while alternate interior angles are on opposite sides of the transversal.

Practice Quiz

Test your knowledge with interactive questions

Lines a and b are parallel.

Which of the following angles are co-interior?

FAQ

Everything you need to know about this question

How do I know which angles are corresponding?

+

Corresponding angles are in the same relative position at each intersection. If one angle is at the top-right of the first intersection, its corresponding angle is at the top-right of the second intersection.

Why are some angles 65° when the given angle is 115°?

+

Adjacent angles on a straight line are supplementary - they add to 180°. So if one angle is 115°, the angle next to it must be $180° - 115° = 65°$ .

What's the difference between vertical and corresponding angles?

+

Vertical angles are opposite each other at the same intersection point and are always equal. Corresponding angles are at different intersection points but in the same relative positions.

Do I need to memorize all the angle relationship names?

+

Focus on understanding the patterns rather than memorizing names. Remember: opposite angles are equal, adjacent angles sum to 180°, and parallel lines create matching angles.

How can I double-check my work?

+

Verify that: (1) All angles around each intersection point sum to 360°, (2) Adjacent angles sum to 180°, and (3) Corresponding angles are equal between the parallel lines.

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Calculate 7 Angles with Parallel Lines: Given Angle 115°

Angle Relationships with Parallel Line Intersections

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know which angles are corresponding?

Why are some angles 65° when the given angle is 115°?

What's the difference between vertical and corresponding angles?

Do I need to memorize all the angle relationship names?

How can I double-check my work?

🌟 Unlock Your Math Potential

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