Answer:
36
Step-by-step explanation:
The angles of a pentagon sum to 180(5-2) = 540 degrees, so each angle of a regular pentagon is 540/5 = 108. Therefore, three of these angles sum to $3 * 108 = 324, which means the indicated angle measures 360 - 324 = 36.
Answer:
Step-by-step explanation:
The diagram of the triangles are shown in the attached photo.
1) Looking at ∆AOL, to determine AL, we would apply the sine rule
a/SinA = b/SinB = c/SinC
21/Sin25 = AL/Sin 105
21Sin105 = ALSin25
21 × 0.9659 = 0.4226AL
AL = 20.2839/0.4226
AL = 50
Looking at ∆KAL,
AL/Sin55 = KL/Sin100
50/0.8192 = KL/0.9848
50 × 0.9848 = KL × 0.8192
KL = 49.24/0.8192
KL = 60
AK/Sin25 = AL/Sin 55
AKSin55 = ALSin25
AK × 0.8192 = 0.4226 × 50
AK = 21.13/0.8192
AK = 25.8
2) looking at ∆AOC,
Sin 18 = AD/AC = 18/AC
AC = 18/Sin18 = 18/0.3090
AC = 58.25
Sin 85 = AD/AB = 18/AB
AB = 18/Sin85 = 18/0.9962
AB = 18.1
To determine BC, we would apply Sine rule.
BC/Sin77 = 58.25/Sin85
BCSin85 = 58.25Sin77
BC = 58.25Sin77/Sin85
BC = 58.25 × 0.9744/0.9962
BC = 56.98
Generally, you are told to approach these by "clearing fractions". That is, you generally multiply the equations by the least common denominator so all fractions and mixed numbers become integers.
Alternatively, you can simply do the arithmetic using the numbers given. You learned a long time ago how to add, subtract, multiply, and divide mixed numbers and fractions. Do these operations as necessary to solve the equations.
Answer:
60
Step-by-step explanation:
Let the original number be x.
According to the question we can write as (2/3)x+20x
On rearranging x−(2/3)x=20
Now taking the L.C.M od 1 and 3 is 3
(3x−2x)/3=20
x/3=20
Again by transposing x=60
So the original number is 60
