Answer:
64 degrees
Step-by-step explanation:
Since the triangles are similar they have the same angle measures
∠P = ∠S ∠R =∠U ∠Q=∠T
We know 2 of the angle measures: ∠S and ∠R, and since they are similar we know ∠P and ∠U
In triangles the sum of all angle measures is always 180 degrees, so we can solve for ∠Q with this formula
subtract 116 from both sides
Therefore ∠Q is equal to 64 degrees
Answer:
The third score must be larger than or equal to 72, and smaller than or equal 87
Step-by-step explanation:
Let's name "x" the third quiz score for which we need to find the values to get the desired average.
Recalling that average grade for three quizzes is the addition of the values on each, divided by the number of quizzes (3), we have the following expression for the average:
SInce we want this average to be in between 80 and 85, we write the following double inequality using the symbols that include equal sign since we are requested the average to be between 80 and 85 inclusive:
Now we can proceed to solve for the unknown "x" treating each inaquality at a time:
This inequality tells us that the score in the third quiz must be larger than or equal to 72.
Now we study the second inequality to find the other restriction on "x":
This inequality tells us that the score in the third test must be smaller than or equal to 87 to reach the goal.
Therefore to obtained the requested condition for the average, the third score must be larger than or equal to 72, and smaller than or equal 87: