Calculate Angle D in ABCD Deltoid: Given Angles 30° and 40°

Kite Angle Properties with Interior Calculations

ABCD Deltoid.

Calculate the size of D ∢D .

AAABBBDDDCCC3040

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find angle D
00:07 Adjacent sides are equal in a kite
00:11 In an isosceles triangle, base angles are equal
00:23 The sum of angles in a triangle equals 180
00:33 Let's substitute appropriate values according to the given data
00:53 Let's collect terms and isolate D
01:13 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

ABCD Deltoid.

Calculate the size of D ∢D .

AAABBBDDDCCC3040

2

Step-by-step solution

The side angles in a kite are equal, therefore:

B=C=70 B=C=70

Also, therefore:

ACB=30 ACB=30

BCD=40 BCD=40

Now we can calculate angle A. Since the sum of angles in a triangle is 180, this is done as follows:

1803030=120 180-30-30=120

Now we can calculate angle D. As we know, the sum of angles in a kite is 360, so:

3601207070=100 360-120-70-70=100

D=100 D=100

3

Final Answer

100

Key Points to Remember

Essential concepts to master this topic
  • Property: Opposite angles in a kite are supplementary (add to 180°)
  • Technique: Use angle sum 360° - 120° - 70° - 70° = 100°
  • Check: All four angles: 120° + 70° + 70° + 100° = 360° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all angles in a kite are equal
    Don't treat a kite like a rhombus where all angles are equal = wrong answer like 90°! Kites have two pairs of equal adjacent angles, not four equal angles. Always identify which angles are adjacent and equal based on the kite's symmetry axis.

Practice Quiz

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Indicates which angle is greater

FAQ

Everything you need to know about this question

How is a kite different from other quadrilaterals?

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A kite has two pairs of adjacent equal sides and two pairs of adjacent equal angles. Unlike a rhombus, opposite angles are not necessarily equal!

Why are angles B and C both 70° in this problem?

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In a kite, adjacent angles at the ends of the cross diagonal are equal. Since B and C are at opposite ends of the symmetry axis, they must be equal: B=C=70° ∠B = ∠C = 70°

How do I find the individual angles from the given measurements?

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The diagram shows 30° and 40° which are parts of the angles at B. So ABC=30°+40°=70° ∠ABC = 30° + 40° = 70° , and by kite properties BCD=70° ∠BCD = 70° too.

Can I use the triangle method to find angle A?

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Yes! The diagonal creates triangles. In triangle with the 30° angles: A=180°30°30°=120° ∠A = 180° - 30° - 30° = 120°

What if I get a different answer when checking?

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Double-check that you correctly identified which angles are equal in the kite. Remember: adjacent angles are equal, not opposite ones like in a parallelogram!

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