Triangle 1 has an angle that measures 34° and an angle that measures 48°. Triangle 2 has an angle that measures 34° and an angle that measures a°, where a ≠ 48. Based on the information, Jennifer claims that triangle 1 and triangle 2 cannot be similar. What value of a, in degrees, will refute Jennifer’s claim?

Answer: \( a = 98^\circ \)

Explanation: For two triangles to be similar, they must have the same angles. Triangle 1 has angles of \(34^\circ\), \(48^\circ\), and \(98^\circ\) (since the sum of angles in a triangle is \(180^\circ\)). Triangle 2 has angles \(34^\circ\), \(a^\circ\), and another angle. To refute Jennifer’s claim, \(a\) must be \(98^\circ\) to match the third angle of Triangle 1.

Steps:

1. Sum of Angles in a Triangle: The sum of the angles in any triangle is \(180^\circ\).

1. Calculate Third Angle of Triangle 1:

1. Determine Condition for Similarity:

• Triangle 2 has an angle of \(34^\circ\) and \(a^\circ\).
• For similarity, the third angle must be \(180^\circ - 34^\circ - a^\circ\).

1. Set Condition for Similarity:

• To be similar, Triangle 2 must have angles \(34^\circ\), \(a^\circ\), and the third angle that matches Triangle 1’s \(98^\circ\).
• Therefore, \(a = 98^\circ\).

Thus, setting \(a = 98^\circ\) will make Triangle 2 similar to Triangle 1, refuting Jennifer’s claim.