Find X: Solving Angles Between Parallel Lines with 110° and 105°

Parallel Line Angles with Transversal Properties

110110110105105105XXX

What is the value of X given the angles between parallel lines shown above?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:03 The lines are parallel according to the given
00:08 We'll draw another line parallel to the lines
00:12 The sum of angles on a line equals 180
00:16 Subtract the known angle to find the desired angle
00:27 Alternate interior angles are equal between parallel lines
00:34 These are also alternate interior angles
00:37 The sum of angles equals the angle itself
00:42 Calculate to find X
00:50 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

110110110105105105XXX

What is the value of X given the angles between parallel lines shown above?

2

Step-by-step solution

Due to the fact that the lines are parallel, we will begin by drawing a further imaginary parallel line that crosses the 110 angle.

The angle adjacent to the angle 105 is equal to 75 (a straight angle is equal to 180 degrees) This angle is alternate with the angle that was divided using the imaginary line, therefore it is also equal to 75.

In the picture we are shown that the whole angle is equal to 110. Considering that we found only a part of it, we will indicate the second part of the angle as X since it alternates and is equal to the existing X angle.

Therefore we can say that:

75+x=100 75+x=100

x=11075=35 x=110-75=35

3

Final Answer

35°

Key Points to Remember

Essential concepts to master this topic
  • Parallel Lines: Corresponding and alternate angles are always equal
  • Technique: Use supplementary angles: 180° - 105° = 75°
  • Check: Verify angle sum: 75° + 35° = 110° ✓

Common Mistakes

Avoid these frequent errors
  • Confusing angle relationships
    Don't assume all marked angles are equal = wrong answer! Just because angles look similar doesn't mean they have the same relationship. Always identify if angles are corresponding, alternate, or supplementary before calculating.

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 equal when lines are parallel?

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Corresponding angles (same position) and alternate angles (opposite sides of transversal) are equal. Co-interior angles (same side of transversal) add up to 180°.

Why did we need to find 75° first?

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The 105° angle and its adjacent angle form a straight line, so they must add to 180°. This gives us 180° - 105° = 75°, which we need to find X.

What if I can't see the parallel lines clearly?

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Look for arrow marks or parallel symbols (||) on the lines. The problem will always indicate when lines are parallel, as this is crucial for solving the problem.

Can X be larger than the given angles?

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Not in this case! Since X is part of the 110° angle, it must be smaller. Use the equation: 75°+X=110° 75° + X = 110°

How do I remember all these angle relationships?

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  • Corresponding: Same position, equal angles
  • Alternate: Opposite sides, equal angles
  • Co-interior: Same side, angles sum to 180°

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