Angles P and Q are complementary. If m∠P = 8x + 1 and m∠Q = 9x + 4, what is the measure of each angle?

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;

Putting the value of ∠P and ∠Q,

Now using the value of x, solve ∠P and ∠Q; For ∠P

Putting the value of x,

For ∠Q,

Putting the value of x,

Hence, the value of ∠P and ∠Q are 41° and 49° respectively.

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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°

a: 1/6, j: 1/4

step-by-step explanation: you are welcome

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)