Calculate Angle CDM in a Right Triangle with 50° Base Angle

Angle Relationships with Right Triangle Properties

ABC is a right triangle.

If ABC=50 ∢\text{ABC}=50

Calculate the size of CDM ∢CDM .

AAABBBCCCDDDMMM50

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find CDM
00:07 The sum of angles in a triangle equals 180
00:22 Collect terms and isolate C
00:41 This is angle C
00:51 Now we'll use exactly the same method in triangle CMD to find CMD
01:06 Collect terms and isolate CMD
01:29 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

ABC is a right triangle.

If ABC=50 ∢\text{ABC}=50

Calculate the size of CDM ∢CDM .

AAABBBCCCDDDMMM50

2

Step-by-step solution

Let's begin by observing the triangle ABC, where we are given two angles.

Due to the fact that the sum of angles in a triangle equals 180 we are able to calculate angle C in the following way:

1809050=40 180-90-50=40

Now let's proceed to observe triangle CMD, where we are given two angles.

Given that the sum of angles in a triangle equals 180, we are able to calculate angle CDM in the following way:

1809040=50 180-90-40=50

3

Final Answer

50

Key Points to Remember

Essential concepts to master this topic
  • Triangle Sum: All angles in any triangle always equal 180°
  • Method: Find missing angle: 180° - 90° - 50° = 40°
  • Check: Verify both triangles sum to 180°: 90° + 50° + 40° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Confusing which angle to find first
    Don't jump straight to angle CDM without finding angle C first = wrong triangle used! You need angle ACB (40°) to solve triangle CDM. Always find all angles in the first triangle before moving to the second.

Practice Quiz

Test your knowledge with interactive questions

Indicates which angle is greater

FAQ

Everything you need to know about this question

Why do I need to find angle C before angle CDM?

+

Because angle C in triangle ABC becomes an interior angle in triangle CDM! You need this 40° angle to apply the triangle sum rule in the second triangle.

How do I know which triangle to solve first?

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Always start with the triangle where you have the most known angles. Here, triangle ABC has angles of 90° and 50°, so solve it first to find the missing 40°.

What if I get confused by all the angle markings?

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Focus on one triangle at a time. List the three angles in each triangle separately, then apply the 180° rule. Don't try to solve both triangles simultaneously!

Why does angle CDM equal 50° like angle ABC?

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This happens because both triangles share the same angle relationships! Triangle CDM has a 90° angle and the 40° angle from point C, leaving 180°90°40°=50° 180° - 90° - 40° = 50° for angle CDM.

Can I solve this without finding angle C first?

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No! You need all three angles in triangle ABC to understand the geometry. Skipping angle C means you won't know what angle to use in triangle CDM.

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