Answer:
tan(Q) is Option C : 1
Step-by-step explanation:
Given:
[tex]\angle R = 90^0[/tex]
[tex]\angle OPQ = 135^0[/tex]
To Find:
tan(Q)
Solution:
Step 1: Finding the angle QPR
We know that the [tex]\angle OPQ[/tex] and [tex]\angle QPR[/tex] are supplementary angles. Then the sum of [tex]\angle OPQ[/tex] and [tex]\angle QPR[/tex] must be equal to 180 degrees
So
[tex]\angle OPQ +\angle QPR = 180^0[/tex]
From the figure
[tex]135^0 +\angle QPR = 180^0[/tex]
[tex]\angle QPR = 180^0 - 135^0[/tex]
[tex]\angle QPR = 45^0[/tex]
Step 2: Finding the angle PQR
Now we also know that The "Triangle Sum Theorem states" that the three interior angles of any triangle add up to 180 degrees.
According to this theorem , In the figure,
the sum of all the interior angles in the triangle PQR
[tex]\angle P +\angle Q +\angle R = 180^0[/tex]
Substituting the known values
[tex]45^0 +\angle Q +90^0 = 180^0[/tex]
[tex]\angle Q +135^0 = 180^0[/tex]
[tex]\angle Q = 180^0 - 135^0[/tex]
[tex]\angle Q = 45^0[/tex]
Step 3: Finding the tan(Q)
We now Know that [tex]\angle Q = 45^0[/tex]
[tex]tan(Q) = tan(45^0) = 1[/tex]
