Parallel Lines Geometry: Find Angle X Using 53° and 94° Measures

Angle Relationships with Linear Pair Properties

The angles below are between parallel lines.

XXX535353949494

What is the value of X?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:08 The sum of angles on a line equals 180
00:18 Subtract the known angle to find the desired angle
00:31 The sum of angles in a triangle equals 180
00:38 Add up the angles and solve to find X
00:51 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

The angles below are between parallel lines.

XXX535353949494

What is the value of X?

2

Step-by-step solution

Our initial objective is to find the angle adjacent to the 94 angle.

Bearing in mind that adjacent angles are equal to 180, we can calculate the following:

18094=86 180-94=86
Let's now observe the triangle.

Considering that the sum of the angles in a triangle is 180, we can determine the following:

180=x+53+86 180=x+53+86

180=x+139 180=x+139

180139=x 180-139=x

x=41 x=41

3

Final Answer

41°

Key Points to Remember

Essential concepts to master this topic
  • Linear Pairs: Adjacent angles on a straight line sum to 180°
  • Technique: Find 180° - 94° = 86°, then use triangle angle sum
  • Check: Verify 41° + 53° + 86° = 180° in triangle ✓

Common Mistakes

Avoid these frequent errors
  • Using 94° directly in triangle calculations
    Don't use the 94° angle as one of the triangle's interior angles = wrong answer of 33°! The 94° is exterior to the triangle. Always find its adjacent angle (180° - 94° = 86°) first, then use that in your triangle calculations.

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

Why can't I use the 94° angle directly in the triangle?

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The 94° angle is outside the triangle! You need its adjacent angle which forms a linear pair. Since adjacent angles on a line sum to 180°, the interior angle is 180° - 94° = 86°.

How do I know which angles are actually in the triangle?

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Look at the diagram carefully. The triangle's three interior angles are: x, 53°, and the angle adjacent to 94° (which is 86°). The 94° extends outside the triangle.

What if I forget that triangle angles sum to 180°?

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This is a fundamental rule! All triangles, regardless of shape or size, have interior angles that add up to exactly 180°. Write this down: ∠A + ∠B + ∠C = 180°

Can I solve this problem a different way?

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Yes! You could use the exterior angle theorem: an exterior angle equals the sum of the two non-adjacent interior angles. So 94° = x + 53°, giving x = 41°.

How do I identify linear pairs in geometry problems?

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Linear pairs are two adjacent angles that form a straight line. They always add up to 180°. Look for angles that share a vertex and whose non-common sides form a straight line.

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