9514 1404 393
Answer:
6. A
7. 80°
8. 20°
Step-by-step explanation:
6.
It is helpful to read the question and identify the particular parts of the diagram it is asking about.
The corresponding hash marks mean the marked segments are congruent. These show you that ΔMQT is isosceles, so angles QMT and QTM are congruent. The sets of hash marks on NT and SM mean those segments are congruent. Of course MT is congruent to itself.
These facts let you conclude that triangles NTM and SMT are congruent by the SAS theorem. (The base angles of ΔMQT are between the pairs of congruent sides.)
The only answer choice referencing SAS is the first one, choice A.
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7.
Based on the previous question, it is a simple matter to show ΔMPT ≅ ΔTRM by SAS. Then angles MPT and TRM are congruent. Angle MPT is supplementary to angle MPN, so is 180° -100° = 80°.
Angle TRM is congruent to angle MPT, so is 80°.
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8.
With reference to ΔMQN, angle MQT is an external angle. Its measure is equal to the sum of the opposite internal angles QNM and QMN:
∠MQT = ∠NMQ + ∠QNM
95° = 75° + ∠QNM
20° = ∠QNM
From problem 6, we know that angle N is congruent to angle S, so, ...
∠TSR = ∠QNM = 20°
