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
taurus [48]
3 years ago
11

Given: ABCD is a trapezoid, AB=CD, MN is a midsegment, MN=30, BC=17, AB=26 Find: m∠A, m∠B, m∠C, and m∠D

Mathematics
1 answer:
enyata [817]3 years ago
3 0

Answer:

The measures of angle ∠A, ∠B, ∠C, and ∠D are 60, 120, 120 and 60 degree respectively.

Step-by-step explanation:

Given information:AB=CD, MN is a midsegment, MN=30, BC=17, AB=26

Since two opposites sides are equal, therefore we can say that two no parallel sides are equal.

The length of midsegment is average of length of parallel lines.

MN=\frac{AD+BC}{2}

30=\frac{AD+17}{2}

60=AD+17

43=AD

Draw perpendiculars on AD from B and C. Let angle A be θ. D

AD=AE+EF+FD

Since ABCD is an isosceles trapezoid, therefore AE=FD and EF=BC

AD=AE+EF+AE

43=2(AE)+17

26=2(AE)

13=AE

\cos\theta=\frac{base}{hypotenuse}

\cos\theta=\frac{AE}{AB}

\cos\theta=\frac{13}{26}

\cos\theta=\frac{1}{2}

\theta=\cos^{-1}\frac{1}{2}

\theta=60

Since ABCD is an isosceles trapezoid, therefore angles A and D are same. Angle B and C are same.

\angle A=\angle D=60^{\circ}

The sum of two consecutive angles of a trapezoid is 180 degree by consecutive interior angle theorem.

\angle A+\angle B=180^{\circ}

60^{\circ}+\angle B=180^{\circ}

\angle B=120^{\circ}

\angle B=\angle C=120^{\circ}

Therefore measures of angle ∠A, ∠B, ∠C, and ∠D are 60, 120, 120 and 60 degree respectively.

You might be interested in
A television and DVD player cost a total of 1132. The cost of the television is three times the cost of the DVD player. What is
lubasha [3.4K]
Let x rep cost of dvd in $
so the cost of tv is 3x
and x + 3x = 1132
4x=1132
x=1132/4
x= 283 and 3x=3(283)=849
7 0
2 years ago
Can someone please help me on this question! Thank you very much!!
Elis [28]
First find the area of the triangle (on top) and then subtract the area of the circle (on bottom) since the triangle is Equilateral, you can assume that the height can be found by using the 30 60 90 angle relationship. To find the radius of the circle, divide the height by 2.

7 0
3 years ago
Read 2 more answers
Which equation results from adding the equations in this system? Negative 2 x + y = 8. 5 x minus y = negative 5.
skad [1K]

Answer:

x= 1.75 y= 6.75

Step-by-step explanation:

substitution method

3 0
3 years ago
Read 2 more answers
How many millilteres are in 2 and a 1\2
andrew11 [14]

Answer:600 mL 2.54 Cups 2 and 1/2 cups

Step-by-step explanation:

3 0
2 years ago
V varies inversely with the square of t and when t = 6, V = 49. Find t when V = 36 <br><br>t=​
PolarNik [594]

Answer:

49

Step-by-step explanation:

when you follow the instructions and there will be k; k is constant. so t=36 so you through then k will be 1764.

8 0
3 years ago
Other questions:
  • Does anyone know this?
    5·1 answer
  • Can someone help with #3 and show your work !!
    10·2 answers
  • a positive number is 7 times another number if 3 is added to both the numbers then one of the new number becomes 5 by 2 times th
    5·1 answer
  • Use the gcf of 48 and 30 to write the sum of the two numbers as the product of their gcf and another sum
    13·1 answer
  • Which statement is true?
    12·1 answer
  • The isosceles triangle ABC has an area of 48 square units if AB=12 what is the perimeter of Abc in units?
    6·1 answer
  • The number of dogs at the animal shelter is 150 less than the number of
    11·1 answer
  • Find the zeros of the function f(x) = 2x^2 - 10x + 7.9 to the nearest hundredth.
    9·1 answer
  • 28 + 24 as a product of two factors using the GCF and the distributtive property
    14·1 answer
  • -3/8 divided by -2/3
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!