1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Annette [7]
3 years ago
13

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

te and solve a system of equations to find the measures of all the angles.
Mathematics
1 answer:
emmainna [20.7K]3 years ago
4 0

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.

You might be interested in
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are
Alla [95]

sample 1=1 rock=1,200songs

5 0
3 years ago
Expan and simplify the following expression:<br> 3(2a + 3)(2a - 1) - 4 (a^2 - 7)
Mekhanik [1.2K]
= 3(4a^2 + 4a - 3) - 4a^2 + 28
= 12a^2 + 12a - 9 - 4a^2 + 28
= 8a^2 + 12a + 19
= 4a(2a + 3) + 19
3 0
3 years ago
HELP PLEASE I really don’t understand it
valina [46]

Answer:

i think its b

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
What is 82×68 this is very hard
zubka84 [21]

Answer:

5576

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Hey You <br> YES YOU CAN ANSWER THIS PLEASE<br> solve for T: 4 j= -9T
OLEGan [10]
-9T means -9 x T
So if T is equivalent to 4,
you should do:
-9 x 4 = -36
J= -36
8 0
3 years ago
Other questions:
  • NEED HELP!! WILL GIVE BRAINLIEST!!
    8·2 answers
  • What is the value of x
    9·1 answer
  • An item has a price tag of $35 and another tag that says 20% off what is the sale price?
    6·1 answer
  • The height of a building is 1417 ft. How long would it take an object to fall to the ground from the top? Use the formula s = 16
    11·1 answer
  • !!!!!!!PLEASE HELP I NEED THIS FOR TODAY!!!!!
    9·1 answer
  • I need help with these in order!!!​
    7·1 answer
  • 78 – 24 divided by (14 – 6) x 2
    5·1 answer
  • 4.
    13·1 answer
  • Factorise pls explain me i will make u brainlinst​
    9·1 answer
  • 15cm<br> 12cm<br> Shown is a right-angled triangle.<br> Work out the area of the triangle
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!