Question

22
triangle a has two interior angles that measure 24° and 76°. triangle b has two interior angles that measure 24° and 80°. which one of the following statements is true?
a triangle a is similar to triangle b because the interior angles of the two triangles have the same measures.
b triangle a is not similar to triangle b because the interior angles of the two triangles do not have the same
c triangle a is not similar to triangle b because one interior angle of triangle b is greater than that of triangle a.
d there is not enough information to determine whether the two triangles are similar or not.

Explanation:

Step1: Find third angle of Triangle A

Sum of triangle angles is $180^\circ$.
$\text{Third angle of A} = 180^\circ - 24^\circ - 76^\circ = 80^\circ$

Step2: List all angles of Triangle A

Angles of A: $24^\circ, 76^\circ, 80^\circ$

Step3: Find third angle of Triangle B

$\text{Third angle of B} = 180^\circ - 24^\circ - 80^\circ = 76^\circ$

Step4: List all angles of Triangle B

Angles of B: $24^\circ, 76^\circ, 80^\circ$

Step5: Compare angles for similarity

Triangles are similar if all corresponding angles are equal. Both triangles have identical angle measures.

Answer:

A. Triangle A is similar to triangle B because the interior angles of the two triangles have the same measures.