Question

1. two complementary angles are expressed as 4x - 16 and 2x + 10. find the number of degrees in each angle. what is the measure of each angle? try it out 3 what is the angle relationship? what does it mean?

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$.

Step2: Set up the equation

$$(4x - 16) + (2x + 10) = 90$$

Step3: Simplify and solve for $x$

Combine like terms: $6x - 6 = 90$
Add 6 to both sides: $6x = 96$
Divide by 6: $x = \frac{96}{6} = 16$

Step4: Calculate first angle

Substitute $x=16$ into $4x-16$:
$4(16) - 16 = 64 - 16 = 48$

Step5: Calculate second angle

Substitute $x=16$ into $2x+10$:
$2(16) + 10 = 32 + 10 = 42$

Step6: Verify angle relationship

Complementary angles are two angles whose measures add up to $90^\circ$. This means the pair of angles together form a right angle.

Answer:

Angle relationship: Complementary angles; this means the sum of the two angles equals $90^\circ$.
Measure of first angle: $48^\circ$
Measure of second angle: $42^\circ$