35 POINTS WILL MARK BRAINLIEST
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Answer:
Step-by-step explanation:
When two lines cross each other , then the opposite angles are known as vertical angles.
Vertical angles are equal.
Here, ∠A and ∠B are vertical angles.
So, ∠A = ∠B
If and
Then ,
Subtract 5x from both sides, we get
Add 11 on both sides, we get
Now ,
Hence, the measure of
Purple color figure is similar to the original figure.
<u>Solution:</u>
Property of similar polygon:
<em>Similar polygons have same shape, corresponding angles are congruent and the corresponding sides are in the same ratio.</em>
(1) <u>Compare original figure with green color figure:</u>
Angles of the original figure:
37°, 53° and 90°.
Angles of the green color figure:
67°, 23° and 90°
These two angles of the triangles not congruent angles.
Hence these shapes are not similar.
(2) <u>Compare original figure with yellow color figure:</u>
Angles of the original figure:
37°, 53° and 90°.
Angles of the yellow color figure:
67°, 23° and 90°
These two angles of the triangles are not congruent angles.
Hence these shapes are not similar.
(3) <u>Compare original figure with purple color figure:</u>
Angles of the original figure:
37°, 53° and 90°
Angles of the purple color figure:
37°, 53° and 90°
These two triangles have same shape and congruent angles.
Ratio of the sides:
These two triangles have same ratio.
Hence these shapes are similar.
Hence purple color figure is similar to the original figure.