Question

a triangle has interior angles measuring 36° and 112° which triangles are similar to this triangle select true or false for each triangle

Answer 1

Answer:

Triangle with interior angles measuring 36° and 32°

Triangle with interior angles measuring 32° and 112°

Step-by-step explanation:

we know that

If two triangles are similar, then its corresponding angles are congruent

If two triangles have two equal internal angles, then the triangles are similar by AA Similarity Postulate

step 1

Calculate the measure of the third internal angle

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

Let

x------> the measure of the third internal angle

$x\°+36\°+112\°=180\°\\ \\x=180\°-148\°\\ \\x=32\°$

step 2

Verify each triangle

case A) Triangle with interior angles measuring 36° and 32°

Is true -----> by AA Similarity Postulate

case B) Triangle with interior angles measuring 36° and 148°

Is false -----> Is not a triangle because the sum of its internal angles is greater than 180 degrees

case C) Triangle with interior angles measuring 32° and 112°

Is true -----> by AA Similarity Postulate

case D) Triangle with interior angles measuring 112° and 148°

Is false -----> Is not a triangle because the sum of its internal angles is greater than 180 degrees