Answer
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Step-by-step explanation
There are a couple of reasons to conclude that two triangles are similar. One of them is for all the angles of the triangle to all be the same. This is the similar triangle that is most important for these questions.
7) Triangle A is a right angle triangle.
Since the total measure of the angles of a triangle is 180°, and one of the other two angles is given as 40°, the three angles of triangle A are 90°, 40° and 50°
Triangle B is also a right angle triangle.
The angles of triangle B are 90°, 30° and 60°.
Hence, these two triangles aren't similar since the measure of their respective angles are not all the same.
8) The two triangles are isoscelles triangles (the two sides marked have the same lengths and the angles at the base of the marked sides are the same).
So, since the total measure of the angles of a triangle is 180°, the angles of triangle A are 35°, 35° and 110°.
For triangle B, the angles are 35°, 35° and 110°.
Hence, we can conclude that these two triangles are similar since the measures of the angles of triangle A match those of triangle B.
9) These are right angle triangles too.
The measures of the angles of triangle A are 90°, 25° and 65° (must add up to 180°)
The measures of the angles of triangle B are 90°, 15° and 75°.
Hence, it is evident that these two triangles aren't similar because their angles are not the same.
10) If the two triangles are congruent, then the angles at C and F will be similar, that is, the same. So,
2.5x + 8 = 3.5x - 7
3.5x - 7 = 2.5x + 8
3.5x - 2.5x = 8 + 7
x = 15°
Angle F = 3.5x - 7 = 3.5 (15) - 7 = 52.5 - 7 = 45.5°
Angle E can then be calculated
90° + Angle F + Angle E = 180° (Sum of angles in a triangle)
90° + 45.5° + Angle E = 180°
Angle E = 180° - 90° - 45.5°
Angle E = 44.5°
11) The diagram will show similar triangles only if the angles of triangle RSN are the same as those of triangle MLN. Or just establishing that RS is parallel to LM.
Angle L + Angle M + Angle N = 180° (Sum of angles in a triangle)
Angle L + 74° + 32° = 180°
Angle L = 180° - 74° - 32° = 74°
Angle R + Angle S + Angle N = 180°
Angle R + 85° + 32° = 180°
Angle R = 180° - 85° - 32° = 63°
The angles of triangle RSN are 63°, 85° and 32°.
The angles of triangle MLN are 74°, 74° and 32°.
The angles aren't the same, hence, the figure doesn't show simiar triangles.
Hope this Helps!!!