Respuesta :

So the ones that would be true are m<MKQ+m<PKQ=m<PKM and PK is a bisector. These two are the only ones, the first one wouldn't be true, because we don't know if PKQ and QKM are congruent or not so we can't prove if it's a bisector or not. The second one wouldn't be true for the same reason, we aren't given any information about those two angles. The third isn't true because again, we don't know the angle measures or if they are congruent or not. The fourth is true because the segments of an angle add up to the whole angle. The next one is true because we are given the information that <PKM is a right angle and therefore 90° and a straight angle, which <JKM is said to be is 180°. the last one is not true because we don't know the measures of either of the angles and are given nothing about any congruent angles.

The statements that are true are;

3. m∠JKL = 45°

4. m∠MKQ + m∠PKQ = m∠PKM

5. line PK is an angle bisector

This involves various angle bisection theorems.

We are told that Line segment JKM is a straight angle. This means that;

PK is a line drawn perpendicular to line segment JKM at the point K.

  • The first option tells us that; Line KQ is an angle bisector. This statement can't be true because the line line KQ does not pass through the diagonal vertex of the right angled symbol at point K.

  • The second option says that;  ∠LKQ is bisected. This statement is not true because like i stated earlier PK is just a perpendicular line to JKM that bisects it into 2 equal parts and not a bisector of ∠LKQ.

  • The third option says that; m∠JKL = 45°. This statement is true because from the image it is clear that line KL divides m∠PKJ into two equal angles.

  • The fourth option says that; m∠MKQ + m∠PKQ = m∠PKM. This statement is true. Now, although KQ doesn't bisect m∠PKM into 2 equal parts, nevertheless it divides it into 2 angles namely m∠MKQ and m∠PKQ. This means the sum of m∠MKQ + m∠PKQ must yield m∠PKM.

  • The fifth option says that line PK is an angle bisector. This statement is true because we are told that JKM is a straight angle. Thus as PK is perpendicular to it, it has bisected it into two equal parts.

  • The sixth option says that; ∠JKL ≅ ∠QKM. This is not true because as seen earlier ∠JKL is a bisected angle which is 45° whereas, ∠QKM is not a bisected angle and thus not equal to 45°.

read more at; brainly.com/question/16968539

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