The scatter plot drawn at left depicts the price of 1 gallon of gasoline in

The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Wri

emmainna [20.7K]

Answer:

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.

4 0

3 years ago

Three more than twice a number is nine

denis23 [38]

Answer:

2x + 3 = 9

Step-by-step explanation:

Three more than twice a number is nine

Twice a number would be 2x
where x is the number

Three more would be + 3

And is means equal sign or “=“

6 0

3 years ago

Read 2 more answers

Of the students in Rosalie's dance class 29 out of 59 have participation in dance class before. (options)

oksano4ka [1.4K]

Answer:

I would believe its 1/2

5 0

4 years ago

E

Evgesh-ka [11]

Answer:

He bought 20 shirts

Step-by-step explanation:

shirts -- x

pants -- 3/4 of x

Therefore,

He bought --- 28(3/4 of x) pants and 40(x) shirts.

So, 28(3/4 of x) + 40(x) = 1220

=> 21x + 40x = 1220

=> 61x = 1220

=> x = 20

He bought 20 shirts and 15 pants.

Thenks and meak me brainliest :))

3 0

3 years ago

Can someone check this out to see if I have this correct? If not can you help me out please? Thank you! The answers are on 2nd p

nataly862011 [7]

Answer:

Answer 1; Angles forming a linear sum to 180°

Answer 2; Substitution

Answer 3; Definition of perpendicular lines

Step-by-step explanation:

The two column proof is presented as follows;

Statement ${}$ Reason

1. ∠SWT ≅ ∠TWU ${}$ Given

2. m∠SWT + m∠TWU = 180° ${}$ Angles forming a linear sum to 180°

3. m∠SWT + m∠SWT = 180° ${}$ Substitution

4. m∠SWT = 90° ${}$ Algebra

5. $\underset{TV}{\leftrightarrow }$ ⊥ $\underset{SU}{\leftrightarrow }$ ${}$ Definition of perpendicular lines

Perpendicular lines are defined as lines that are at right angles (90°) to each other, therefore given that the angle formed by the lines $\underset{TV}{\leftrightarrow }$ and $\underset{SU}{\leftrightarrow }$ m∠SWT = 90°, therefore, the lines $\underset{TV}{\leftrightarrow }$ and $\underset{SU}{\leftrightarrow }$ are perpendicular to each other.

3 0

3 years ago