The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.

a. i. x + y = 180  (1) and  x - 4y = 5   (2)

ii. The two acute angles are 35° each and the two obtuse angles are 145° each.

Step-by-step explanation:

a. The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.

i. Write a system of equations to find the measures of all the angles.

Let x be the obtuse angles and y be the acute angles.

Since we have two obtuse angles at the top of the isosceles trapezoid and two acute angles at the bottom of the isosceles trapezoid, and also, since the sum of angles in a quadrilateral is 360, we have

2x + 2y = 360

x + y = 180  (1)

Its is also given that the measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles.

So, x = 4y + 5   (2)

x - 4y = 5   (2)

So, our system of equations are

x + y = 180  (1) and  x - 4y = 5   (2)

ii. Solve a system of equations to find the measures of all the angles.

Since

x + y = 180  (1) and  x - 4y = 5   (2)

Subtracting (2) from (1), we have

x + y = 180  (1)

-

x - 4y = 5   (2)

5y = 175

dividing both sides by 5, we have

y = 175/5

y = 35°

From (1), x = 180° - y = 180° - 35° = 145°

So, the two acute angles are 35° each and the two obtuse angles are 145° each.

the answer is: d) o, f, and kr.

atomic radius of bromine (br) is 114 pm.

atomic radius of oxygen (o) is 73 pm.

atomic radius of fluorine (f) is 72 pm.

atomic radius of krypron (kr) is 112 pm.

the atomic radius of a chemical element is a measure of the size of its atom.

the atomic radius varies with increasing atomic number, but usually increases because of increasing of number of electrons.

the atomic radius decreases across the periods because an increasing number of protons, because greater attraction between the protons and electrons.