Calculate Angle ABC: Using 92° and 131° in Parallel Lines Configuration

Q: How do I know which angles are alternate angles?

Alternate angles are on opposite sides of a transversal and between parallel lines. They form a Z-pattern when you connect them. In this diagram, the 92° angle and angle ABH are alternate angles.

Q: What are supplementary angles and how do I use them?

Supplementary angles add up to 180°. When two angles form a straight line, they're supplementary. Here, angle CBH and the 131° angle are supplementary, so CBH = 180° - 131° = 49°.

Q: Why do I need to add the two angles together?

Angle ABC is made up of two smaller angles: ABH and CBH. Since point H lies on line segment AC, these angles are adjacent and their measures add up to give the total angle ABC.

Q: How can I identify parallel lines in a diagram?

Look for arrow markers or identical markings on lines. In geometry problems, parallel lines are usually indicated by these symbols. The problem also states there are parallel lines.

Q: What if I can't see the angle clearly in the diagram?

Focus on the relationships between angles rather than trying to measure visually. Use properties like alternate angles, corresponding angles, and supplementary angles to find the answer mathematically.

Q: Can I solve this problem a different way?

Yes! You could also use corresponding angles or co-interior angles depending on which angle relationships you identify first. The key is recognizing that angle ABC is split into two parts.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate angle ABC

00:05 The lines are parallel according to the given data

00:12 Alternate angles on parallel lines are equal

00:27 The lines are parallel according to the given data

00:35 The sum of the corresponding angles between the parallel lines is 180

00:48 Insert the appropriate values according to the given data and solve for the angle

00:55 Isolate angle HBC

01:05 This is angle HBC

01:12 The entire angle equals the sum of its parts

01:17 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Observe the diagram below.

Calculate the size of angle ABC.

2

Step-by-step solution

In the given drawing we observe three parallel lines as well as two lines that intersect them.

We are asked to determine the size of angle ABC,

We can identify that the angle is actually composed of two angles, angle ABH and CBH.

In fact, we will calculate the size of each angle separately and combine them together.

Angle A is an alternate angle to angle ABH, and since alternate angles are equal, angle ABH equals 92.

Angle CBH is supplementary to angle DCB, supplementary angles equal 180, therefore we can calculate:

$HBC = 180-DCB$

$HBC = 180 - 131$

$HBC = 49$

Now that we have found angles ABH and CBH, we can add them together to find angle ABC

$ABH + CBH = ABC$

$92 + 49 = 141$

3

Final Answer

$141$

Key Points to Remember

Essential concepts to master this topic

Rule: Alternate angles are equal when lines are parallel
Technique: Split angle ABC into ABH (92°) + CBH (49°)
Check: Verify supplementary angles: 131° + 49° = 180° ✓

Common Mistakes

Avoid these frequent errors

Assuming angle ABC equals one of the given angles directly
Don't think angle ABC = 92° or 131° directly = wrong answer! The angle ABC is composed of two separate angles that must be calculated individually. Always identify if an angle is split into parts and calculate each part separately.

Practice Quiz

Test your knowledge with interactive questions

If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

How do I know which angles are alternate angles?

+

Alternate angles are on opposite sides of a transversal and between parallel lines. They form a Z-pattern when you connect them. In this diagram, the 92° angle and angle ABH are alternate angles.

What are supplementary angles and how do I use them?

+

Supplementary angles add up to 180°. When two angles form a straight line, they're supplementary. Here, angle CBH and the 131° angle are supplementary, so CBH = 180° - 131° = 49°.

Why do I need to add the two angles together?

+

Angle ABC is made up of two smaller angles: ABH and CBH. Since point H lies on line segment AC, these angles are adjacent and their measures add up to give the total angle ABC.

How can I identify parallel lines in a diagram?

+

Look for arrow markers or identical markings on lines. In geometry problems, parallel lines are usually indicated by these symbols. The problem also states there are parallel lines.

What if I can't see the angle clearly in the diagram?

+

Focus on the relationships between angles rather than trying to measure visually. Use properties like alternate angles, corresponding angles, and supplementary angles to find the answer mathematically.

Can I solve this problem a different way?

+

Yes! You could also use corresponding angles or co-interior angles depending on which angle relationships you identify first. The key is recognizing that angle ABC is split into two parts.

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Calculate Angle ABC: Using 92° and 131° in Parallel Lines Configuration

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