What is the arc measure of arc (DE) in degrees?

Mathematics

1 answer:

Nastasia [14]3 years ago

6 0

Answer:

m(arc)ED = 39 degrees

Step-by-step explanation:

The measure of an arc of a circle is equal to the measure of the central angle that intercepts it.

BE is a diameter. That means that m<BPE = 180.

AC is a diameter. That means that m<APC = 180.

Let's start with angle BPE to find w:

m<BPE = m<BPA + m<EPA = 180

4w + 8 + 4w + 4 = 180

8w + 12 = 180

8w = 168

w = 21

Now we deal with angle APC:

m<APC = m<APE + m<EPD + m<DPC = 180

4w + 4 + m<EPD + 2w + 11 = 180

6w + 15 + m<EPD = 180

m<EPD + 6w = 165 Equation 1

Now we use w = 21 in Equation 1.

m<EPD + 6w = 165

m<EPD + 6(21) = 165

m<EPD + 126 = 165

m<EPD = 39

Since the arc measure equals the measure of the central angle that intersects it, m(arc)ED = 39 degrees

Answer: m(arc)ED = 39 degrees

You might be interested in

30 POINTS! Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 3

Vesna [10]

C^2= a^2 + b^2 a=b
34^2= a^2 + a^2
1156=2a^2
a^2=1156/2
a^2=578
a=24.04

The side length is 24.04
Or I got this also
Using the special triangle theorem , an isosceles triangle has a diagonal equal to the square root of 2 of the legs of the triangle. In this case, the length of the legs is 34/ sqrt of 2 or equal to 24.04 units . This rule is based on the Pythagorean theorem
If the length of each side = x.

By Pythagoras' Theorem:

x² + x² = 34²

2x² = 34²

x² = 34² / 2

x² = 578

x = √578

x ≈ 24.04 inches
hope this helps

3 0

3 years ago

Jack and Rebecca Pearson just had triplets. They want to have enough money for their

Marianna [84]

Answer:

a) $12,440.43

b) $8,000.00

c) $4,440.43

Step-by-step explanation:

the question is a bit ambiguous, I calculated from zero initial Deposit to $100 per quarter. If they deposited $100 initially and then $100 quarterly for 20 years then the numbers are as follows.

a) $12,671.05

b) $8,100

c) $4,571.05