Find Angle B in a Quadrilateral with Angles 80°, 95°, and 45°

Q: Why do quadrilateral angles add up to 360° instead of 180°?

A quadrilateral can be divided into two triangles by drawing a diagonal. Since each triangle has angles that sum to 180°, the quadrilateral's total is 2 × 180° = 360°!

Q: What if I accidentally used 180° in my calculation?

If you calculated $ ∢B = 180° - 220° $, you'd get -40°, which is impossible! Negative angles tell you that you used the wrong formula. Always use 360° for quadrilaterals.

Q: Does this work for any quadrilateral shape?

Yes! Whether it's a square, rectangle, trapezoid, or irregular quadrilateral like in this problem, the interior angles always sum to 360°.

Q: How can I remember the difference between triangles and quadrilaterals?

Use this memory trick: TRIangle = 3 sides = 180° (3 × 60°). QUADrilateral = 4 sides = 360° (4 × 90°).

Quadrilateral Angle Sum with Three Known Angles

ABCD is a quadrilateral.

$∢A=80$

$∢C=95$

$∢D=45$

Calculate the size of $∢B$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate angle B

00:06 The sum of angles in any quadrilateral is always equal to 360

00:18 Substitute appropriate values according to the given data

00:37 Group terms and isolate B

01:10 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

ABCD is a quadrilateral.

$∢A=80$

$∢C=95$

$∢D=45$

Calculate the size of $∢B$ .

Step-by-step solution

We know that the sum of the angles of a quadrilateral is 360°, that is:

$A+B+C+D=360$

We replace the known data within the following formula:

$80+B+95+45=360$

$B+220=360$

We move the integers to one side, making sure to keep the appropriate sign:

$B=360-220$

$B=140$

Final Answer

140°

Key Points to Remember

Essential concepts to master this topic

Rule: All quadrilateral interior angles sum to exactly 360°
Technique: Add known angles first: 80° + 95° + 45° = 220°
Check: Verify sum equals 360°: 80° + 140° + 95° + 45° = 360° ✓

Common Mistakes

Avoid these frequent errors

Using triangle angle sum (180°) instead of quadrilateral sum
Don't use 180° for quadrilaterals = missing angle calculations will be 180° too small! This happens because students confuse triangle and quadrilateral properties. Always remember quadrilaterals have four sides, so their angles sum to 360°.

Practice Quiz

Test your knowledge with interactive questions

Find the measure of the angle $\alpha$

FAQ

Everything you need to know about this question

Why do quadrilateral angles add up to 360° instead of 180°?

A quadrilateral can be divided into two triangles by drawing a diagonal. Since each triangle has angles that sum to 180°, the quadrilateral's total is 2 × 180° = 360°!

What if I accidentally used 180° in my calculation?

If you calculated $∢B = 180° - 220°$ , you'd get -40°, which is impossible! Negative angles tell you that you used the wrong formula. Always use 360° for quadrilaterals.

Does this work for any quadrilateral shape?

Yes! Whether it's a square, rectangle, trapezoid, or irregular quadrilateral like in this problem, the interior angles always sum to 360°.

How can I remember the difference between triangles and quadrilaterals?

Use this memory trick: TRIangle = 3 sides = 180° (3 × 60°). QUADrilateral = 4 sides = 360° (4 × 90°).

What if the problem doesn't show me a diagram?

The diagram helps visualize, but you don't need it! As long as you know it's a quadrilateral with four angles, just use the $A + B + C + D = 360°$ formula.

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Find Angle B in a Quadrilateral with Angles 80°, 95°, and 45°

Quadrilateral Angle Sum with Three Known Angles

❤️ 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

Why do quadrilateral angles add up to 360° instead of 180°?

What if I accidentally used 180° in my calculation?

Does this work for any quadrilateral shape?

How can I remember the difference between triangles and quadrilaterals?

What if the problem doesn't show me a diagram?

🌟 Unlock Your Math Potential

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