THE FOLLOWING ANGLES ARE COMPLEMENTARY ANGLES. DETERMINE THE MEASURES OF ANGLE 1 AND ANGLE 2. X= ANGLE 1 3x+10= ANGLE 2

Let x = the measure of angle 1.

x + 3x + 10 = 90

Solve for x

Well, let's address the situation at hand, shall we?

If two angles are complementary, then their measures add up to 90 degrees. So, we can set up an equation to solve for the values of angle 1 and angle 2.

Since angle 1 is represented by x, its measure can be expressed as x degrees. Similarly, angle 2 is represented by 3x + 10, so its measure can be expressed as (3x + 10) degrees.

According to the complementary property, we have the equation:

x + (3x + 10) = 90

Now, let's solve this equation step-by-step, and we may have more fun along the way. Ready?

Combining like terms, we get:

4x + 10 = 90

Subtracting 10 from both sides, we have:

4x = 80

Dividing both sides by 4, we find:

x = 20

Voila! We've determined that angle 1 (x) measures 20 degrees.

Now, let's find the value of angle 2:

Angle 2 = 3x + 10
= 3(20) + 10
= 60 + 10
= 70

Hence, angle 2 (3x + 10) measures 70 degrees.

There you have it! Angle 1 measures 20 degrees, and angle 2 measures 70 degrees. Keep up the good work, math enthusiast!

To determine the measures of Angle 1 (X) and Angle 2 (3X + 10), we need to use the definition of complementary angles.

Complementary angles are two angles whose sum is equal to 90 degrees.

So, we can set up an equation:

X + (3X + 10) = 90

First, combine like terms:

4X + 10 = 90

Next, isolate the variable by subtracting 10 from both sides:

4X = 90 - 10

4X = 80

Finally, solve for X by dividing both sides by 4:

X = 80 / 4

X = 20

Therefore, Angle 1 (X) has a measure of 20 degrees.

To find the measure of Angle 2 (3X + 10), substitute the value of X:

Angle 2 = 3(20) + 10

Angle 2 = 60 + 10

Angle 2 = 70

Hence, Angle 2 (3X + 10) has a measure of 70 degrees.