Advertisements
Advertisements
Question
In a pentagon ABCDE, AB is parallel to DC and ∠A: ∠E : ∠D = 3: 4: 5. Find angle E.
Solution
Let the measure of the angles are 3x, 4x and 5x.
Thus
∠A + ∠B + ∠C + ∠D + ∠E = 540°
3x + (∠B + ∠C) + 4x + 5x = 540°
12x + 180° = 540°
12x = 360°
x = 30°
Thus, the measure of angle E will be 4 × 30° = 120°
APPEARS IN
RELATED QUESTIONS
Two alternate sides of a regular polygon, when produced, meet at the right angle.
Find:
(i)The value of each exterior angle of the polygon;
(ii) The number of sides in the polygon.
One angle of a six-sided polygon is 140o and the other angles are equal.
Find the measure of each equal angle.
Find the sum of the interior angles of a polygon of: 12 sides
Is it possible to have a polygon whose each interior angle is 124°?
If the difference between an exterior angle of a regular polygon of 'n' sides and an exterior angle of another regular polygon of '(n + 1)' sides is equal to 4°; find the value of 'n'.
The number of sides of two regular polygons are in the ratio 2 : 3 and their interior angles are in the ratio 9 : 10. Find the number of sides of each polygon.
The ratio between the number of sides of two regular polygon is 3 : 4 and the ratio between their interior angles is 2 : 3. Find the number of sides of each polygon.
Find the value of each angle of an octagon if two of its angles are 148° and 152° and the remaining angles are all equal.
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides of the polygon.
The difference between an exterior angle of (n - 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6°. Find the value of n.
