The angles of a quadrilateral are m, 3m, 2m and 3m in that order. a Write an equation in m. b. Find m c Find the angles of the quadrilateral d Make a sketch of the quadrilateral e. What kind of quadrilateral is it? 2. Calculate the size of each angle of a regular octagon 3. How many sides does a polygon have, if the sum of its angles is 18 right angles? b If the polygon is regular, what is the size of each angles in degrees?
Answers
Answer:
=> A/Q,
m + 3m + 2m + 3m = 360°
9m = 360°
m = 360/9
m = 40°
Angle A = m = 40°
Angle B = 3m = 120°
Angle C = 2m = 80°
Angle D = 3m = 120°
Sketch--> plz make with own..
Angle A = m = 40°
Angle B = 3m = 120°
Angle C = 2m = 80°
Angle D = 3m = 120°
Given : a quadrilateral
To Find: angles of a quadrilateral
Solution:
According to the angle sum property, The sum of all the angles of the quadrilateral is 360°.
Therefore,
Angle A + Angle B + Angle C + Angle D = 360°
m + 3m + 2m + 3m = 360°
9m = 360°
m = 360/9
m = 40°
Implying that,
Angle A = m = 40° , Angle B = 3m = 120° , Angle C = 2m = 80° , Angle D = 3m = 120°
2.)
A regular octagon has eight sides that are equal and eight angles that are equal.
The size of all exterior angles of the regular octagon.
We do this by dividing 360° by the number of sides, which is 8.
360° ÷ 8 = 45°.
Therefore, each angle of the octagon is 45°.
3.)
The sum of the measures of the interior angles
of a convex n-gon (a polygon with n sides)
is (n−2)×180°.
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