Calculate Angle X in Straight Line: Given 41° and 45° Angles

Triangle Angle Sum with Missing Interior Angle

Calculate the value of the angle X.

XXX4145

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate X
00:03 The angles are adjacent, forming a straight angle (sum to 180)
00:06 Add and equate to 180, solve for X
00:09 Collect like terms
00:12 Isolate X
00:14 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

Calculate the value of the angle X.

XXX4145

2

Step-by-step solution

To solve this problem, we will apply the triangle sum theorem:

  • Step 1: Identify the triangle formed by the known angles and the unknown angle X X .
  • Step 2: Use the triangle angle sum property which states: The sum of the angles in a triangle is 180 180^\circ .
  • Step 3: The known angles in the problem are 41 41^\circ and 45 45^\circ .

Now, let's complete the steps:

Step 1: The angles presented form a triangle involving the angles 41 41^\circ , 45 45^\circ , and X X .
Step 2: Apply the triangle angle sum theorem: 41+45+X=180 41^\circ + 45^\circ + X = 180^\circ .
Step 3: Simplifying this we get:

41+45+X=180 41 + 45 + X = 180

86+X=180 86 + X = 180

Solve for X X :

X=18086 X = 180 - 86

X=94 X = 94

Therefore, the value of angle X X is 94 94^\circ .

3

Final Answer

94

Key Points to Remember

Essential concepts to master this topic
  • Triangle Angle Sum: All three interior angles always equal 180°
  • Technique: Add known angles first: 41° + 45° = 86°
  • Check: Verify sum: 41° + 45° + 94° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Using angles that aren't part of the same triangle
    Don't assume all angles in the diagram are interior angles of one triangle = wrong setup! This leads to incorrect equations and wrong answers. Always identify which three angles actually form the triangle vertices before applying the 180° rule.

Practice Quiz

Test your knowledge with interactive questions

Find the measure of the angle \( \alpha \)

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FAQ

Everything you need to know about this question

How do I know which angles belong to the same triangle?

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Look for three angles that meet at the three vertices of a triangle. In this problem, X, 41°, and 45° are the three interior angles that form the triangle.

What if the diagram shows more than three angles?

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Focus only on the interior angles of the triangle you're solving for. Extra angles might be exterior angles or part of other shapes - ignore them for the triangle angle sum.

Why does the triangle angle sum always equal 180°?

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This is a fundamental property of triangles in flat geometry. No matter what size or shape the triangle is, the three interior angles will always add up to exactly 180°.

Can I solve this if one of the given angles was obtuse?

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Yes! The triangle angle sum theorem works for all triangles - acute, right, or obtuse. Just make sure you're identifying the correct interior angles.

What if my calculation doesn't give me a whole number?

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That's fine! Angles can be decimal values or fractions. Just make sure your final answer makes sense (between 0° and 180° for interior angles).

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