Question

Triangle 1 has an angle that measures 34\degree34° and an angle that measures 48\degree48°. Triangle 2 has an angle that measures 34\degree34° and an angle that measures a\degreea°, where a\ne48a=48.Based on the information, Jennifer claims that triangle 1 and triangle 2 cannot be similar.What value of aa, in degrees, will refute Jennifer's claim?

Answer 1

Given:

Triangle 1 Angles: 34°, 48°

Triangle 2 Angles: 34°, a°

Find: the value of "a" that will refute the claim

Solution:

Jennifer claims that the two triangles are not similar. For us to refute this claim, we have to prove that the two triangles can be similar for a certain value of "a".

Recall that the sum of the measures of the interior angles of a triangle is 180°.

If Triangle 1 has angles measuring 34° and 48°, then its third angle must measure 98°.

$180\degree-34\degree-48\degree=98\degree$

For two triangles to be similar, each corresponding angle must be congruent with the other.

Hence, if Triangle 2 has an angle measuring 34° and a° not equal to 48°, then the value of "a" must be 98° in order to make the two triangles similar and refute Jennifer's claim.