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malfutka [58]
2 years ago
11

PLEASE HELP ASAP Given: m∠DEA=46°, m∠P=14°Find the measurements of arc AD and arc BC.

Mathematics
2 answers:
antoniya [11.8K]2 years ago
8 0

Answer:

The measurement of arc AD is 53°

The measurement of arc BC is 39°

Step-by-step explanation:

Let

x----> the measurement of arc AD

y---> the measurement of arc BC

we know that

The measure of the internal angle is the semi-sum of the arcs comprising it and its opposite

so

m∠DEA=(1/2)[x+y]

substitute the value

46°=(1/2)[x+y]

92°=[x+y] -----> equation A

The measurement of the external angle is the semi-difference of the arcs which comprises

m∠P=(1/2)[x-y]

substitute the value

14°=(1/2)[x-y]

28°=[x-y] -----> equation B

Adds equation A and equation B

92°+14°=2x

x=106°/2=53°

Find the value of y

substitute in the equation A the value of x

92°=[53°+y]

y=92°-53°=39°

Nady [450]2 years ago
7 0

Answer: 32 and 60

Step-by-step explanation:

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What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame? 16.7° 17.5° 72.5° 73.3°
umka21 [38]

The complete question is

"A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7°, 17.5°, 72.5°,73.3°"

The value of angle x would be 16.7 degrees.

<h3>What is the right triangle?</h3>

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

The angle of a right angle is always 90 degrees.

In order to find the value of x, a tan would be used.

This is because we have given the opposite and adjacent sides as 10 ft and 3 ft.

Tan Ф = opposite / adjacent

Tan Ф =  (3/10)

= 16.7 degrees

The value of angle x would be 16.7 degrees.

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6 0
1 year ago
Save Work out the size of angle AED.<br> b) Work out x
Mamont248 [21]

Answer:

x = 10°

Step-by-step explanation:

a). Since, opposite angles of a cyclic quadrilateral are supplementary angles"

   Therefore, in cyclic quadrilateral ABDE,

   m∠ABD + m∠AED = 180°

   110° + m∠AED = 180°

   m∠AED = 180° - 110°

                 = 70°

b). AD = ED [Given]

   m∠EAD = m∠AED [Since, opposite angles of equal sides are equal in measure]

   m∠EAD = m∠AED = 70°

   By triangle sum theorem in ΔABD,

   m∠BAD + m∠ABD + m∠ADB = 180°

   m∠BAD + 110° + 40° = 180°

   m∠BAD = 180 - 150

                 = 30°

    m∠AEB = m∠AED + m∠DAB [By angles addition postulate]

    m∠AEB = 70° + 30°          

                  = 100°

    By triangle sum theorem in the large triangle,

    x° + m∠AEB + m∠EAB = 180°

    x° + 100° + 70° = 180°

    x = 180 - 170

    x = 10°

8 0
2 years ago
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