Given:
Measure of angles in triangle 1 = 36 degrees and 51 degrees
Measure of angles in triangle 2 = 36 degrees and a degrees
Where:
a ≠ 51 degrees
Frank claims both triangles cannot be similar.
Let's find the value of a that refutes Frank's claim.
Given:
Sum of the two angles in traingle 1 = 36 + 51 = 87 degrees
Let's find the third angle in triangle 1 by applying triangle angle sum theorem.
180 - (36 + 51) = 180 - 87 = 93 degrees
The third angle in triangle 1 is = 93 degrees
Thus, for the triangles to be similar, let's use the Angle-Angle-Angle simliarity theorem.
Thus, since angle a cannot be 51 degrees, the measure of a will be = 93 degrees
To refute Frank's claim, the value of a will be: 93 degrees
ANSWER:
93 degrees