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

Triangle Deff is shown below. 110°, e, d, f, 135°​-example-1

2 Answers

7 votes

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.

User Mehrad Farahnak
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8 votes

Answer:

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.

Triangle Deff is shown below. 110°, e, d, f, 135°​-example-1
User Zin Yackvaa
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7.1k points