What is the ratio of the number of degrees in the interior angle of a regular pentagon to the number of degrees in the interior angle of a regular hexagon ? express your answer as a common fraction.

Answer is 3/4

Step-by-step explanation: The sum of the interior angles of a regular polygon is calculated as follows;

(n-2) × 180° {where n represents the number of sides of the polygon}

A pentagon is a polygon with five equal sides. Therefore the sum of it's interior angles is calculated as;

(5-2) × 180°

=3×180°

=540°

A hexagon is a polygon with six equal sides. Therefore the sum of it's interior angles is calculated as;

(6-2) × 180°

=4×180°

=720°

Therefore, the ratio of the number of degrees in the interior angles of a regular pentagon, to the number of degrees in the interior angles of a regular hexagon is given as

540:720

If you divide both sides by their prime factors (2×2×3×3×5) the ratio becomes

3:4 in it's simplest form.

As a common fraction, it can be expressed as

3/4.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions