Answer:
B. The triangles are similar.
Step-by-step explanation:
If two triangles are similar, the measures of all 3 angles of one triangle will be congruent to the measures of all 3 angles of the second triangle.
For triangle PQR, the known angles are 66° and 100°. Since the sum of the measures of the angles of a triangle is 180°, this makes the missing angle
180-(66+100) = 180-166 = 14°
For triangle RST, the known angles are 14° and 100°. This makes the missing angle
180-(14+100) = 180-114 = 66°
Since all three angles in PQR are congruent to all three angles in RST, this makes the triangles similar.
The two triangles PQR and triangle RST are congruent, therefore option b is the correct answer that the triangles are similar.
Triangle PQR has two known interior angles of 66° and 100° and Triangle RST has two known interior angles of 14° and 100°.
The interior angles are those angles that lie inside the shape. The sum of the interior angles of the triangle is always 180°.
Triangle RST has two known interior angles of 14° and 100°.
here, the third interior angle let's say x
x + 14° + 100°= 180°
x = 66°
Similarly,
Triangle PQR has two known interior angles of 66° and 100°.
the third angle let's say z
So, z + 66° + 100° =180°
z = 14°
Therefore, we can see that the three interior angles of the triangle are the same.
The two triangles are said to be congruent if the measure of all the angles of the triangle is congruent to the measure of all the angles of another triangle.
Hence, The two triangles PQR and triangle RST are congruent, the option b is the correct answer that the triangles are similar.
Learn more about the congruent triangles here:
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