The measure of angles 1, 2, 3 are - [tex]90^{o} ,\;63^{0} ,\;63^{0}[/tex].
Consider the figure attached.
We have a labelled kite similar to mentioned in the question. We have angle ABO = [tex]27^{o}[/tex].
We have to find the measure of angle 1, 2, 3.
State the properties of kite.
Here are some of the properties of kite -
- The diagonals of a kite intersect each other at [tex]90^{o}[/tex] angle.
- There are two pairs of equal length sides which are adjacent to each other.
According to the question -
In ΔAOB,
[tex]\angle2 + \angle ABO+\angle AOB = 180^{o} \\\angle2+27^{o} +90^{o}=180^{o}\\\angle2+117^{o} =180^{o}\\\angle2 = 63^{o}[/tex]
Th, the two angles opposite to the two equal sides are also equal, since BA and BC are equal, therefore - [tex]\angle2=\angle3[/tex][tex]=63^{o}[/tex].
Since the diagonals of the kite intersect each other perpendicularly, therefore -
[tex]\angle1=90^{o}[/tex]
Hence the measure of angles 1, 2, 3 are - [tex]90^{o} ,\;63^{0} ,\;63^{0}[/tex].
To solve more questions on Kites, visit the link below -
https://brainly.com/question/24260949
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