Angle angle similarity needs two corresponding angles in two triangles to be same. The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~
How to find measure of missing third angle in a triangle?
It is a theorem in mathematics that sum of internal angles of a triangle equate to [tex]180^\circ[/tex]
Suppose that two angles are given as [tex]a^\circ[/tex] and [tex]b^\circ[/tex] and let there is one angle missing. Let its measure be [tex]x^\circ[/tex]
Then, by the aforesaid theorem, we get:
[tex]a^\circ + b^\circ + x^\circ = 180^\circ\\\\ \text{Subtracting a + b degrees from both sides} \\\\x^\circ = 180^\circ - (a^\circ + b^\circ)[/tex]
What is Angle-Angle similarity for two triangles?
Two triangles are similar if two corresponding angles of them are of same measure. It is because when two pairs of angles are similar, then as the third angle is fixed if two angles are fixed, thus, third angle pair also gets proved to be of same measure. This makes all three angles same and thus, those two triangles are scaled copies of each other. Thus, they're called similar.
For given case, we've got
[tex]m\angle K = m\angle R\\m\angle J = m\angle Q\\[/tex]
Thus, for the rest of the angle pair, we have:
[tex]m\angle L = 180 - (m\angle J + m\angle K) = 180 - (m\angle Q + m\angle R) = m\angle P\\\\m\angle L = m\angle P[/tex]
Thus, given two triangles are similar by angle-angle similarity.
Thus,
The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~
Learn more about angle-angle similarity here:
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