Question

Explain why m<1>m<3.which statement below can be made, according to the corollary to the Triangle Exterior Angle Theorem?

Answer 1

In the given image you have that m∠1 is lower than angle m∠3 becasue it is clear that angle ∠1 is an angle greater than 90° and angle ∠3 is lower than 90°. Then m∠1 > m∠3.

Now, in order to determine which of the given statements is true for the given figure, you take into account that the exterioir angle theorem stablishes that the measure of an exterior angle of the triangle is greater that any of the measure of the remote interioir angles of the triangle.

Thus, you can notice that the measure of the external angle ∠1 is greater than the measure either angle ∠4 or angle ∠2.

Hence, following statement is true:

m∠1 > m∠4 and m∠1 > m∠2