Right Triangle Angle Calculation: Finding Angle C Given A = 20°

Q: How do I know which angle is the right angle?

Look for the square symbol in the diagram! This marks the $ 90° $ angle. In this problem, angle B has the square, so $ ∢B = 90° $.

Q: Why do the other two angles add up to 90°?

Since all triangle angles sum to $ 180° $ and one angle is already $ 90° $, the remaining two must add up to $ 180° - 90° = 90° $!

Q: What if I'm given angle C instead of angle A?

The same principle applies! If $ ∢C = 35° $, then $ ∢A = 90° - 35° = 55° $. Just subtract the given angle from $ 90° $.

Q: Do I need to use trigonometry for this problem?

Not at all! This is purely about angle relationships. You don't need sine, cosine, or tangent - just the fact that complementary angles in a right triangle sum to $ 90° $.

Right Triangle Angles with Given Acute Angle

ABC is a right triangle.

$∢A=20°$

Is it possible to calculate the size of $∢C$ ?

If so, what is it?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find angle C together.

00:13 Remember, the sum of angles in a triangle is always 180 degrees.

00:23 Now, plug in the values you have been given.

00:34 Next, collect the terms and solve for angle C.

00:58 And there you have it! That's how we find the missing angle.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

ABC is a right triangle.

$∢A=20°$

Is it possible to calculate the size of $∢C$ ?

If so, what is it?

Step-by-step solution

To solve this problem, we need to determine the measure of angle $∢C$ in the right triangle $\triangle ABC$ where angle $∢A = 20°$ .

Since $\triangle ABC$ is a right triangle, we know that one angle, $∢B$ , is $90°$ . Hence, the other two angles, $∢A$ and $∢C$ , must sum to $90°$ as well.

We are given that $∢A = 20°$ . Therefore, we can set up the equation: $∢A + ∢C = 90°$

Substitute the given value of $∢A$ into the equation:
$20° + ∢C = 90°$

To solve for $∢C$ , subtract $20°$ from both sides:
$∢C = 90° - 20°$

Thus, we find that:
$∢C = 70°$

Therefore, the size of angle $∢C$ is $\textbf{70°}$ .

Final Answer

Yes, 70°.

Key Points to Remember

Essential concepts to master this topic

Angle Sum Rule: All angles in any triangle sum to $180°$
Right Triangle Property: One angle is $90°$ , so other two sum to $90°$
Check: Verify $20° + 70° + 90° = 180°$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting which angle is the right angle
Don't assume angle A or C is the right angle = wrong calculation! The diagram shows angle B is $90°$ (marked with a square). Always identify the right angle first, then use $∢A + ∢C = 90°$ .

Practice Quiz

Test your knowledge with interactive questions

Is DE side in one of the triangles?

FAQ

Everything you need to know about this question

How do I know which angle is the right angle?

Look for the square symbol in the diagram! This marks the $90°$ angle. In this problem, angle B has the square, so $∢B = 90°$ .

Why do the other two angles add up to 90°?

Since all triangle angles sum to $180°$ and one angle is already $90°$ , the remaining two must add up to $180° - 90° = 90°$ !

What if I'm given angle C instead of angle A?

The same principle applies! If $∢C = 35°$ , then $∢A = 90° - 35° = 55°$ . Just subtract the given angle from $90°$ .

Can I solve this without knowing it's a right triangle?

No - you need to know it's a right triangle! Without this information, there are infinitely many possible values for angle C. The right angle constraint is essential.

Do I need to use trigonometry for this problem?

Not at all! This is purely about angle relationships. You don't need sine, cosine, or tangent - just the fact that complementary angles in a right triangle sum to $90°$ .

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Right Triangle Angle Calculation: Finding Angle C Given A = 20°

Right Triangle Angles with Given Acute Angle

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know which angle is the right angle?

Why do the other two angles add up to 90°?

What if I'm given angle C instead of angle A?

Can I solve this without knowing it's a right triangle?

Do I need to use trigonometry for this problem?

🌟 Unlock Your Math Potential

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