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Vlad [161]
4 years ago
11

∠ADB and ∠BDC represent a linear pair because points A, D, and C lie on a straight line. Calculate the sum of m∠ADB and m∠BDC. T

hen move point B around and see how the angles change. What happens to the sum of m∠ADB and m∠BDC as you move point B around?
Mathematics
2 answers:
brilliants [131]4 years ago
7 0
If points A, D and C lie on a straight line, then angles ∠ADB and ∠BDC are supplementary angles and
m\angle ADB+m\angle BDC=180^{\circ}.
1. If you move point B right from the initial position, then m∠ADB increases and m∠BDC decreases, but m\angle ADB+m\angle BDC=180^{\circ}.
2. If you move point B left from the initial position, then m∠ADB decreases and m∠BDC increases, but m\angle ADB+m\angle 
BDC=180^{\circ}.
3. When point B lie on the line ADC, then:
a. Point B lies on the right hand from point D: m\angle ADB=180^{\circ} \\m\angle BDC=0^{\circ};
b. Point B lies on the left hand from point D: m\angle ADB=0^{\circ} \\m\angle BDC=180^{\circ}.
4. When point B is reflected about the line ADC situation is the same as in parts 1 and 2.

Conclusion: m\angle ADB+m\angle BDC=180^{\circ}.








mixer [17]4 years ago
6 0

Answer:

The sum of m∠ADB and m∠BDC remains the same: m∠ADB + m∠BDC = 180°.

Step-by-step explanation:

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6 0
3 years ago
Instructions:Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Svetllana [295]

Answer:

D = 108°

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H = 252°

I = 288°


Explanation:

Every regular polygon with <em>n </em>sides can be divided into <em>n</em>  congruent triangles. The angle with vertex the center of the polygon will measure 360 : <em>n </em>degrees. This will also be the angle of rotation under which the polygon matches itself.

We are given a regular decagon, therefore:

<em>n </em>= 10

α = 360 : <em>n </em>= 36°


We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.

A' will coincide with D after three rotations: 3 × 36° = 108°

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