Calculate the size of the unmarked angle:160

It is not possible to calculate.

Calculate the Unmarked Angle: Finding the Missing Value in a 160° Ray Diagram

Q: Why do adjacent angles always add up to 180°?

When two angles share a vertex and their outer rays form a straight line, they create what's called a linear pair. A straight line measures exactly 180°, so the two angles must add up to this total.

Q: How can I tell if angles are adjacent?

Adjacent angles must share a common vertex (corner point) and have a common side between them. They should not overlap - just touch along their shared ray.

Q: Can I use this method for any angle pair?

Only for linear pairs (adjacent angles on a straight line). Other angle relationships like vertical angles or complementary angles have different rules.

Q: What if I get a negative answer when subtracting?

Check if you subtracted correctly: 180° minus the given angleVerify the given angle is less than 180°Make sure you're looking at the right angle in the diagram

Adjacent Angles with Linear Pair Properties

Calculate the size of the unmarked angle:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the value of the empty angle

00:03 A straight angle equals 180

00:06 Therefore subtract the known angle from it to find the empty angle

00:09 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the size of the unmarked angle:

Step-by-step solution

The unmarked angle is adjacent to an angle of 160 degrees.

Remember: the sum of adjacent angles is 180 degrees.

Therefore, the size of the unknown angle is:

$180-160=20$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Linear Pair Rule: Adjacent angles on a straight line sum to 180°
Subtraction Method: Calculate $180° - 160° = 20°$ for unknown angle
Verification: Check that $160° + 20° = 180°$ forms straight line ✓

Common Mistakes

Avoid these frequent errors

Adding angles instead of subtracting from 180°
Don't add 160° + unknown angle = wrong approach! This ignores the linear pair rule and leads to impossible angle measures over 180°. Always subtract the known angle from 180° to find the adjacent angle.

Practice Quiz

Test your knowledge with interactive questions

a is parallel to b.

Calculate the angles shown in the diagram.

FAQ

Everything you need to know about this question

Why do adjacent angles always add up to 180°?

When two angles share a vertex and their outer rays form a straight line, they create what's called a linear pair. A straight line measures exactly 180°, so the two angles must add up to this total.

How can I tell if angles are adjacent?

Adjacent angles must share a common vertex (corner point) and have a common side between them. They should not overlap - just touch along their shared ray.

What if the given angle was larger than 180°?

That's impossible! An angle in a linear pair cannot exceed 180° because the total must equal 180°. If you see this, check your diagram interpretation or calculations.

Can I use this method for any angle pair?

Only for linear pairs (adjacent angles on a straight line). Other angle relationships like vertical angles or complementary angles have different rules.

What if I get a negative answer when subtracting?

Check if you subtracted correctly: 180° minus the given angle
Verify the given angle is less than 180°
Make sure you're looking at the right angle in the diagram

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