Angle 1 and Angle 2 are supplementary. Angle 1 is 20 degree less than nine times the size of angle 2.

Mathematics

1 answer:

nadya68 [22]3 years ago

5 0

Answer:

∠1=160° and ∠2=20°

Step-by-step explanation:

Let ∠1 = x

∠2 = y

as these two angles are supplementary their sum is 180

that x+y=180 ----(A)

Also given that ∠1 is 20 degree less than nine times the size of ∠2.

Hence

x=9y-20

putting value of x in A and solving for y

9y-20+y=180

10y=180+20

10y=200

y=10

Putting this y in A

x+10=180

x=160

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Find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of a regular dodecagon.

IgorLugansk [536]

See the picture to better understand the problem

we know that
A regular dodecagon has 12 sides
Central angle of a regular polygon is an angle whose vertex is the center of the polygon with two consecutive radii
thus
the measure of a central angle is
m∠AOC=360/n
where n is the number of sides
so
m∠AOC=360/12-----> 30°

therefore

the answer Part a) is
the measure of the angle formed by two consecutive radii is 30 degrees

Part b)
we know that
OAC is an isosceles triangle
so
OA=OC
m∠OAC=m∠OCA

the sum of the internal angles of a triangle is 180 degrees
so
180=2*m∠OAC+m∠AOC-----> m∠OAC=[180-30]/2----> 75°

the answer part b) is
the measure of the angle formed by a radius and a side is 75°