Answer:
Using the given information, the measurement of ∠P is 41° and the measurement of ∠Q is 49°
Step-by-step explanation:
Complementary angles are angles that have a sum measurement of 90°. So, the measurement of ∠P and the measurement of ∠Q will have a sum of 90° because they are complementary angles.
So, let's set up an equation where we add the two measurements and equal them to 90.
(8x + 1) + (9x + 4) = 90
Combine like terms.
17x + 5 = 90
Subtract 5 from both sides of the equation.
17x = 85
Divide 17 from both sides of the equation.
x = 5
Now that we have the value of x, let's plug in this value for each angle to find their measurement.
m∠P = 8(5) + 1 = 40 + 1 = 41
m∠Q = 9(5) + 4 = 45 + 4 = 49
So, the measurement of ∠P is 41° and the measurement of ∠Q is 49°
The value of ∠P=41° and ∠Q= 49°.
Given to us:
∠P = 8x + 1,
∠Q = 9x + 4,
Complementary angles are the angles whose measures sums to 90°.
As given in the question ∠P and ∠Q are complementary angles, therefore we can write it as;
[tex]\angle P + \angle Q = 90^o[/tex]
Putting the value of ∠P and ∠Q,
[tex](8x + 1) + (9x + 4) = 90\\17x + 5 = 90\\17x = 90 - 5\\\\x = \dfrac{85}{17}\\\\x= 5[/tex]
Now using the value of x, solve ∠P and ∠Q; For ∠P
[tex]\angle P= 8x+1\\[/tex]
Putting the value of x,
[tex]\angle P= 8x+1\\\angle P= (8\times 5 )x+1\\\angle P= 40+1\\\angle P= 41[/tex]
For ∠Q,
[tex]\angle P= 9x+4\\[/tex]
Putting the value of x,
[tex]\angle Q= 9x+4\\\angle Q= (9\times 5 )x+4\\\angle Q= 45+4\\\angle Q= 49[/tex]
Hence, the value of ∠P and ∠Q are 41° and 49° respectively.
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