With proving theorems 20 points 1. if two vertical angles are supplementary, what is the measure of each angle?

Remember that when two angles are vertical angles, their angle measurements are the same, as the angles are congruent.

Note the Vertical Angle Theorem. Angles vertically opposite (directly opposite) when two lines intersect are congruent with each other.

Now note that supplementary means 180°

Set the equation. Let the angles = x

2x = 180

Isolate the x. Note the equal sign. What you do to one side, you do to the other. Divide 2 from both sides

(2x)/2 = (180)/2

x = 180/2

x = 90

90° is the measurement of each angle.

~Rise Above the Ordinary

The population of quail after 2 years is 337.74

Step-by-step explanation:

The initial population of quail = i =295

The rate of increase of population = r = 7%

The population of quail after 2 years = f

The time period of increase population = t = 2 years

Now, According to question

The population of quail after 2 years =  initial population of quail ×

Or, f = i ×

Or, f = 295 ×

Or, f = 295 × (1.07)²

Or, f = 295 × 1.1449

∴  f = 337.745

So, The population of quail after 2 years = f = 337.74

Hence, The population of quail after 2 years is 337.74 Answer