Quadrilateral ABCD is a rhombus with diagonals AC and BD. if angle M equals 25 find the measures of angles 2 , 3 , 4 and 5
I have no idea where angle M and angles 2,3,and 4 are
Since you make a point of stating there are two diagonals, I can only assume that angle M is intended to be angle CAD or BAC or their opposites on the diagonaly opposite vertex.
If M was intended to be angle BAD or BCD, there would be no need to identify the diagonals.
We also have no idea what angles 1, 2, 3 and 4 are.
If /_CAD is 25º, then /_CAB = /_BCA = /_DCA also = 25º. Angles ABC and ADC = 130º.
If /_ BAD = 25º, then so is /_BCD. Angles ABC and ADC = 155º.
If the measure of ÐDAB = 50°, and ÐDAC = 20°, what is ÐCAB?
the diagonal of a parallograms
To find the measures of angles 2, 3, 4, and 5 in quadrilateral ABCD, we need to use the properties of a rhombus.
First, let's locate the angles in the diagram.
A--------2---------B
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3| |4
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D--------5---------C
Angle M is provided as 25°. Since ABCD is a rhombus, opposite angles are equal. Therefore, angle 1 is also 25°.
A---1---B
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D---1---C
Now let's find angles 2 and 4.
Angle 2 and angle 4 are adjacent angles next to angle 1. Adjacent angles in a rhombus are supplementary, meaning their sum is 180°.
Therefore, angle 2 + angle 1 = 180°.
angle 2 + 25° = 180°.
Subtract 25° from both sides.
angle 2 = 180° - 25° = 155°.
Similarly, angle 4 + angle 1 = 180°.
angle 4 + 25° = 180°.
Subtract 25° from both sides.
angle 4 = 180° - 25° = 155°.
A------2-------B
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4| |4
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D------5-------C
Now let's find angles 3 and 5.
Angle 3 and angle 5 are opposite angles in a rhombus, so they are equal.
Angle 1 + angle 5 + angle 3 = 180°.
25° + angle 5 + angle 3 = 180°.
Subtract 25° from both sides.
angle 5 + angle 3 = 155°.
Since angle 5 and angle 3 are equal, we can write:
2(angle 5) = 155°.
Divide both sides by 2.
angle 5 = 155° / 2 = 77.5°.
Therefore, angle 3 is also 77.5°.
A-------2-------B
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4| |4
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D--------5--------C
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3| |3
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In summary, the measures of angles in quadrilateral ABCD are as follows:
Angle 1 = 25°
Angle 2 = 155°
Angle 3 = 77.5°
Angle 4 = 155°
Angle 5 = 77.5°