If m<1=53 degrees, what is m<3. David states that DEF is an isosceles triangle. Is he correct. Explain

Subtract this result from 180 to get the value of angle 3. This is because angle 2 and angle 3 are supplementary angles. They are a linear pair (aka the angles form a straight line)

angle3 = 180 - (angle2)

angle3 = 180 - 37

angle3 = 143 degrees

note: you can add the remote interior angles at D and E to get 90+53 = 143 and you get the same answer. This is using the exterior angle theorem.

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Part 2

In order for the triangle to be isosceles, the two acute angles (angle 1, angle 2) must be congruent. Call them x for now. They must also add to 90, so x+x = 90 leads to 2x = 90 and solves to x = 45. Both angle 1 and angle 2 must be 45 degrees. However, angle 1 is 53 degrees and angle 2 is 37 degrees. So that is why David's statement is not correct.

alokdubeyvidyaatech alokdubeyvidyaatech · Answer 2 · 2021-11-14T07:03:24+01:00

David states that DEF is an isosceles triangle.

David's statement is not correct.

Part 1

∠1 and angle ∠2 are complementary angles. They add to 90°.

So, ∠1 + ∠2 = 90°

53° +∠2 = 90°

∠2 = 90° - 53°

∠2 = 37°

Subtract this result from 180° to get the value of ∠3. This is because ∠2 and ∠3 are supplementary angles. They are a linear pair (the angles form a straight line).

∠3 = 180° - ∠2

∠3 = 180° - 37°

∠3 = 143°

note: you can add the remote interior angles at D and E to get 90+53 = 143 and you get the same answer. This is using the exterior angle theorem.

Part 2

In order for the triangle to be isosceles, the two acute angles (∠1, ∠2) must be congruent. Call them x for now. They must also add to 90°, so x+x = 90° leads to 2x = 90° and solves to x = 45°. Both angle 1 and angle 2 must be 45 degrees. However, angle 1 is 53 degrees and angle 2 is 37 degrees. So that is why David's statement is not correct.

Therefore, David's statement is not correct.

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