Question

△PQR and △RST share point R. P R and Q R are congruent, and T R and S T are congruent. What is m∠TSR?

a) m∠TSR = 90 degrees
b) m∠TSR = 60 degrees
c) m∠TSR = 120 degrees
d) m∠TSR = 45 degrees

Answer 1

The measure of angle TSR in triangle PQR and triangle RST is 60 degrees.

Step-by-step explanation:

The question asks for the measure of angle TSR in triangle PQR and triangle RST, given that PR and QR are congruent, and TR and ST are congruent.

Since PR and QR are congruent, angle PQR and angle QPR are also congruent. Similarly, since TR and ST are congruent, angle STR and angle RTS are also congruent.

Therefore, angle TSR is congruent to angle STR and angle RTS. Based on the information given, we can conclude that m∠TSR = m∠STR = m∠RTS. Since the sum of angles in a triangle is 180 degrees, we have:

m∠TSR + m∠STR + m∠RTS = 180 degrees

Substituting m∠TSR = m∠STR = m∠RTS, we get:

3m∠TSR = 180 degrees

m∠TSR = 180 degrees / 3 = 60 degrees