Question

topics: angle addition postulate, segment addition postulate, congruent angles, angle classification, congruent segments, midpoints, angle bisectors

directions: read each question carefully. for problems with diagrams, use the figure provided. assume all diagrams are not drawn to scale. show all work. good luck!

1. if $\angle xyz + \angle zyr = \angle xyr$, which postulate is used?

a) angle addition postulate
b) segment addition postulate
c) midpoint theorem
d) vertical angles theorem

1. if $\angle abc = 40^\circ$ and $\angle cbd = 50^\circ$, find $\angle abd$.

a) $80^\circ$
b) $90^\circ$
c) $100^\circ$
d) $120^\circ$

1. if $\angle jkl$ is split by ray $km$ into $\angle jkm = 28^\circ$ and $\angle mkl = 62^\circ$, find $\angle jkl$.

a) $30^\circ$
b) $80^\circ$
c) $90^\circ$
d) $120^\circ$

1. if $\angle pqr = 135^\circ$ and $\angle pqs = 45^\circ$, what is $\angle sqr$?

a) $45^\circ$
b) $75^\circ$
c) $90^\circ$
d) $100^\circ$

1. which equation represents the segment addition postulate?

a) $ab = bc$
b) $ab + bc = ac$
c) $ab \times bc = ac$
d) $ac - bc = 2ab$

Explanation:

Question 1

Step1: Recall postulates

The Angle Addition Postulate states that if a point lies in the interior of an angle, the sum of the two smaller angles equals the larger angle. Here, \( \angle XYZ + \angle ZYR=\angle XYR \) fits this. The Segment Addition Postulate is for segments, Midpoint Theorem about midpoints, Vertical Angles Theorem about vertical angles (equal), so not relevant.

Step1: Apply Angle Addition Postulate

\( \angle ABD=\angle ABC + \angle CBD \)

Step2: Substitute values

\( \angle ABC = 40^\circ \), \( \angle CBD = 50^\circ \), so \( \angle ABD=40^\circ+ 50^\circ = 90^\circ \)

Step1: Apply Angle Addition Postulate

\( \angle JKL=\angle JKM+\angle MKL \)

Step2: Substitute values

\( \angle JKM = 28^\circ \), \( \angle MKL = 62^\circ \), so \( \angle JKL = 28^\circ+62^\circ=90^\circ \)

Answer:

a) Angle Addition Postulate

Question 2