Need help step by step plz
1 answer:
I'm assuming D is the center of the circle. See the new figure.
Angle BDC = 106 degrees, that's the definition of arc measure.
Triangle BDC is isosceles (two radii make congruent sides) so the two remaining angles in BDC are equal, DBC=DCB=(180-106)/2=37 degrees.
Angle BAC = 106/2 = 53 degrees, subtending the arc of 106 degrees.
Angle CAD = 53/2 = 26.5 degrees because AD is a bisector, the shared hypotenuse of congruent right triangles AED and AFD.
AFD is also congruent to CFD, so angle DCA is also 26.5 degrees
Angle ACB is the sum of DCA and DCB, ACB = 26.5 + 37 = 63.5 degrees
The angle subtends the arc we seek, whose measure must be double:
10x - 23 = 2(63.5) = 127 degrees
10x = 150
x = 15
Answer: 15
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Answer:
The value of N is 4
Step-by-step explanation:
∵ The perimeter of any figure is the sum of its sides
∵ The sides of an irregular pentagon are (x+8), (x+6), (x+4), (x+2), x
∴ Its perimeter = x + 8 + x + 6 + x + 4 + x + 2 + x
→ Add the like terms
∴ Its perimeter = 5x + 20 ⇒ (1)
∵ The formula for the perimeter of an irregular pentagon is 5(x + N)
∴ The formula of the perimeter = 5(x + N) = 5(x) + 5(N)
∴ The formula of the perimeter = 5x + 5N ⇒ (2)
→ Equate (1) and (2)
∴ 5x + 20 = 5x + 5N
→ Subtract 5x from both sides
∵ 5x - 5x + 20 = 5x - 5x + 5N
∴ 20 = 5N
→ Divide both sides by 5
∴
∴ 4 = N
∴ The value of N is 4