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
Tom [10]
3 years ago
13

If ABCD is a rectangle, calculate x as a function of α

Mathematics
2 answers:
shusha [124]3 years ago
7 0

Answer:

x = 90 - 2α

Step-by-step explanation:

Solution:-

- Consider the right angled triangle " ABD ". The sum of angles of an triangle is always "180°".

                       < BAD > + < ADB > + < ABD > = 180°

                       < ABD > = 180 - 90° - α

                        < ABD > = 90° - α

- Then we look at the figure for the triangle "ABE". Where " E " is the midpoint and intersection point of two diagonals " AC and BD ".

- We name the foot of the perpendicular bisector as " F ":  " BF " would be the perpendicular bisector. The angle < BAE > is equal to < ABD >.

                    < ABD > = < BAE >  = 90° - α   ... ( Isosceles triangle " BEA " )

Where, sides ( BE = AE ).

- Use the law of sum of angles in a triangle and consider the triangle " BFA " as follows:

                     < ABF> + < BFA > + < BAF > = 180°

                     < ABF > = 180 - (90° - α) - 90°

                    < ABF > = α  

Where,       < BAF > = < BAE >

- The angle < ABD > = < ABE > is comprised of two angles namely, < ABF > and < FBE >  = x.

                        < ABD > = < ABE > = < ABF > + x

                         90° - α = α + x

                        x = 90 - 2α   ... Answer

Yanka [14]3 years ago
4 0

Answer:

Step-by-step explanation:

The length of this triangle is 10 squares

and the width is 4 squares

The diagonals divide the rectangle into four triangles

These traingles are isoceles

Each two triangles facing each others are identical

<B = 90 degree

B = alpha + Beta

Let Beta be the angle next alpha

The segment that is crossing Beta is its bisector since it perpendicular to the diagonals wich means that:

Beta = 2x

Then B = alpha + 2x

90 = alpha +2x

90-alpha = 2x

x = (90-alpha)/2

You might be interested in
One of the legs of a right triangle measures 15 cm and the other leg measures 10 cm. Find the measure of the hypotenuse. If nece
Olenka [21]

Answer:

18.0 (use 18 if 18.0 is not an answer choice)

Step-by-step explanation:

15²+10²=225+100 = 325

√325 = 18.028 or 18.0 (use 18 if 18.0 is not an answer choice)

6 0
3 years ago
Read 2 more answers
Please Help! Knowing the negative sign (–) also means "opposite", how do you we read this expression, -8 • 2?
ycow [4]
The answer is -12468
7 0
3 years ago
Read 2 more answers
Help please anyone! Brainliest reward it counting on it!
Viefleur [7K]
X1 + x2  / 2 , y1 + y2 / 2

8 + x2 /2 = 6

So x  is 4

9 + y2 /2 = 6

So y is 3.

Answer is B ( 4, 3)

Please Mark Brainliest if it helped
4 0
3 years ago
I just need to know how to do these questions in the picture above^?
Sav [38]
In the second one I'm pretty sure you just measure the length of the points.
5 0
3 years ago
Read 2 more answers
2
nignag [31]

Answer:

1st = 4×10 ^-9

2nd= 4×10^1

3rd = 4×10^7

4th = 4×10^-5

Step-by-step explanation:

for whole numbers you just have to count from the ending till the number indicated beside the x10

for decimals you count from the front starting at the decimal till you cover the whole number

6 0
1 year ago
Other questions:
  • What formula do you use to prove that a triangle is a right triangle?
    6·1 answer
  • What is an expression containing variables,numbers, and operation symbols?
    8·1 answer
  • eder needs 6 cookies and 2 brownies for every 4 plates he makes how many wikl eder need for 10 plates
    13·1 answer
  • To place and as in a newspaper, it cost $8 plus $0.75 for each line. Write and evaluate an expression to find the total cost for
    5·1 answer
  • Write a wordy problem for b = 2a - 6
    7·1 answer
  • Simplify 18m^0 / 18^0
    5·1 answer
  • 2 3 • 2 4 is equal to _____.
    7·1 answer
  • Find a recursive rule for the nth term of the sequence.<br><br> 5, 20, 80, 320, ...
    8·1 answer
  • Andres buys 3 boxes of markers. Each box has the same number of markers. Andres now has 15 markers. Write and solve an equation
    9·2 answers
  • A local Starbucks is tracking the purchases made by its customers. On Saturday 60% of the customers who purchased donuts also pu
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!