Question

Triangle Deff is shown below. 110°, e, d, f, 135°​

Answer 1

A triangle similar to DEF would possess angles measuring 45 degrees, 70 degrees, and 65 degrees, reflecting the angle relationships established through the theorems.

The angles of a triangle can be determined using various angle relationships. In this case, the given angles a, b, and c are found by applying the Linear Pair of Angles and Triangle Sum Theorem.

For angle a, the Linear Pair of Angles is used: a + 110° = 180°, leading to a = 70°.

Similarly, for angle b, b + 135° = 180°, yielding b = 45°.

Applying the Triangle Sum Theorem to find angle c, 45° + 70° + c = 180°, resulting in c = 65°.

Therefore, a triangle similar to DEF would possess angles measuring 45 degrees, 70 degrees, and 65 degrees, reflecting the angle relationships established through the theorems.

Answer 2

Explanation:

a° + 110° = 180° [Linear pair of angles]

a = 180° - 110°

a = 70°

b° + 135° = 180° [Linear pair of angles]

b = 180° - 135°

b = 45°

a + b + c = 180° [Triangle sum theorem]

45° + 70° + c = 180°

c = 180° - 115°

c = 65°

Therefore, a triangle similar to DEF will have an angle that measures 45 degrees, an angle that measures 70 degrees and an angle that measures 65 degrees.