Find ∠CAD in a Right Triangle with 61° and 17° Angles

Angle Relationships with Triangle Angle Sum

ΔABD is a right-angled triangle.

CAD=? ∢\text{CAD}=\text{?}

AAABBBDDDCCC6117

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find angle CAD
00:05 The sum of angles in a triangle equals 180
00:18 Let's gather terms and isolate A
00:41 This is angle A
00:47 Part of the angle equals the total angle minus the second part
01:04 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

ΔABD is a right-angled triangle.

CAD=? ∢\text{CAD}=\text{?}

AAABBBDDDCCC6117

2

Step-by-step solution

If we look at triangle ABD, we can see that we are given two angles: 90° and 17°.

Since the sum of all angles in a triangle equals 180°, we can calculate angle BAD as follows:

1809017=73 180-90-17=73

Since we know angle BAC, we can calculate angle CAD as follows:

7361=12 73-61=12

3

Final Answer

12°

Key Points to Remember

Essential concepts to master this topic
  • Triangle Rule: All three angles in any triangle sum to 180°
  • Technique: Find missing angle first: 180° - 90° - 17° = 73°
  • Check: Verify angle subtraction: 73° - 61° = 12° for ∠CAD ✓

Common Mistakes

Avoid these frequent errors
  • Trying to find ∠CAD directly without finding ∠BAD first
    Don't attempt to use only the given angles 61° and 17° to find ∠CAD directly = wrong approach! You need the complete angle ∠BAD first. Always find the missing triangle angle using the 180° sum, then subtract the known part.

Practice Quiz

Test your knowledge with interactive questions

Look at the angles shown in the figure below.

What is their relationship?

\( \)αβ

FAQ

Everything you need to know about this question

Why can't I just subtract 61° from 17° to get the answer?

+

Those angles aren't directly related! The 61° is part of a larger angle, and 17° is at a completely different vertex. You need to find the whole angle ∠BAD first.

How do I know which angles to use for the 180° rule?

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Look for a complete triangle! In triangle ABD, you have the right angle (90°), the 17° angle, and one unknown angle. These three must sum to 180°.

What if I forgot that angle A was split into two parts?

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Always examine the diagram carefully! When you see a line like AC inside triangle ABD, it divides angle A into smaller angles. The 61° is just one piece of the larger angle.

Can I solve this problem without using the triangle angle sum?

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No! The triangle angle sum (180°) is essential here. It's the only way to find the complete angle ∠BAD, which you need to subtract 61° from.

Why is the answer 12° and not something else?

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Follow the steps: Triangle ABD has angles that sum to 180°, so ∠BAD = 180° - 90° - 17° = 73°. Since ∠BAC = 61°, then ∠CAD = 73° - 61° = 12°.

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