Find Alpha Angle: Triangle with 69° and 23° Angles

Triangle Angle Sum with Two Known Angles

Find the measure of the angle α \alpha

696969AAABBBCCC23

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the value of A
00:03 The sum of angles in a triangle equals 180
00:06 Substitute in the appropriate values according to the given data and proceed to solve for A
00:10 Collect like terms
00:14 Isolate A
00:19 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the measure of the angle α \alpha

696969AAABBBCCC23

2

Step-by-step solution

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

Therefore, we will use the following formula:

A+B+C=180 A+B+C=180

Now let's input the known data:

α+69+23=180 \alpha+69+23=180

α+92=180 \alpha+92=180

We'll move the term to the other side and keep the appropriate sign:

α=18092 \alpha=180-92

α=88 \alpha=88

3

Final Answer

88

Key Points to Remember

Essential concepts to master this topic
  • Triangle Rule: Sum of all three angles always equals 180 degrees
  • Technique: Add known angles first: 69 + 23 = 92 degrees
  • Check: Verify by adding all three: 88 + 69 + 23 = 180 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting that triangle angles sum to 180°
    Don't assume angles can add to any number = wrong answer like 115°! Students often forget this fundamental rule and just guess. Always remember the triangle angle sum is exactly 180 degrees, then subtract the known angles.

Practice Quiz

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Is DE side in one of the triangles?
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FAQ

Everything you need to know about this question

Why do triangle angles always add to 180 degrees?

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This is a fundamental property of triangles in flat (Euclidean) geometry. No matter what shape or size triangle you have, the three interior angles will always sum to exactly 180°!

What if I get a negative angle?

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Check your arithmetic! Angles in a triangle are always positive. If you get negative, you likely made a calculation error or the given angles don't form a valid triangle.

Can any two angles work in a triangle?

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No! The sum of any two angles must be less than 180°. In this problem, 69° + 23° = 92°, which is less than 180°, so it works.

How do I know which angle is alpha?

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Look at the diagram carefully! α \alpha is marked at vertex A (the top point). The other angles are labeled with their degree measures: 69° and 23°.

What if I forget the triangle angle sum formula?

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Remember it this way: A triangle has 3 angles, and they always add to 180°. You can write it as A+B+C=180° A + B + C = 180° or α+69°+23°=180° \alpha + 69° + 23° = 180° .

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