If ∡PQR=141°
and ∡PQS=(13x+4)°
and ∡SQR=(10x−1)°
, find ∡SQR
(1 point)
∡SQR=
To find ∡SQR, we first need to set up an equation using the given angles.
We know that ∡PQR = ∡PQS + ∡SQR.
Substituting the given angles into this equation, we have:
141° = (13x+4)° + (10x-1)°.
Now, we can combine like terms:
141° = 23x + 3.
Next, we can isolate the variable:
23x = 141° - 3.
Simplifying further, we have:
23x = 138°.
Finally, we can solve for x by dividing both sides of the equation by 23:
x = 138° / 23 = 6°.
Now that we have the value of x, we can substitute it back into the equation ∡SQR = 10x-1°:
∡SQR = 10(6°) - 1° = 60° - 1° = 59°.
Therefore, ∡SQR = 59°.
If QS−→ bisects ∠PQT
. If ∡SQT = (8x−25)°
and ∡PQT = (9x+34)°
find the measure of ∠PQT
(2 points)
∡PQT
=
If QS−→
bisects ∠PQT
. If ∡SQT =
(8x−25)°
and ∡PQT =
(9x+34)°
find the measure of ∠PQT
. The diagram is not to scale.
(2 points)
∡PQT
=
(1 point)
∡DEF=
I'm sorry, but I cannot provide the measure of angle ∡DEF without any given information about its measure.
Since QS−→ bisects ∠PQT, we can set up an equation using the given angles:
∡SQT = ∡PQT.
Substituting the given angles into this equation, we have:
8x-25 = 9x+34.
To solve for x, we can subtract 8x from both sides of the equation:
-25 = x + 34.
Next, we can subtract 34 from both sides:
-59 = x.
Now that we have the value of x, we can substitute it back into the equation ∡PQT = 9x+34° to find the measure of ∠PQT:
∡PQT = 9(-59) + 34°.
Evaluating this expression, we get:
∡PQT = -531 + 34° = -497°.
However, angles cannot have negative measures, so we discard this solution. Therefore, there is no valid measure for ∠PQT given the given values for ∡SQT and ∡PQT.
Since QS bisects ∠PQT, we know that ∡SQT is equal to ∡PQT. Therefore, we can set up an equation:
∡SQT = ∡PQT
Substituting the given angles, we have:
8x - 25 = 9x + 34
To solve for x, we can subtract 8x from both sides:
-25 = x + 34
Next, subtract 34 from both sides:
-59 = x
Now we can substitute the value of x back into the equation ∡PQT = 9x + 34 to find the measure of ∠PQT:
∡PQT = 9(-59) + 34 = -531 + 34 = -497
However, angles cannot have negative measures. This means that there is no valid measure for ∠PQT given the given values for ∡SQT and ∡PQT.