Advertisements
Advertisements
Question
If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then find the measure of the smallest angle.
Solution
We have, ∠A : ∠B : ∠C :∠D = 3 : 5 : 9 : 13 .
So, let ∠A = 3x,
∠B = 5x,
∠C = 9x
and ∠D = 13x
By angle sum property of a quadrilateral, we get:
∠A + ∠B + ∠C + ∠D = 360
3x + 5x + 9x + 13x = 360
30x = 360
`x =(360)/(30) `
x = 12
Smallest angle is :
∠A = 3x
∠A = 3(12°)
∠A = 36°
Hence, the smallest angle measures 36°.
APPEARS IN
RELATED QUESTIONS
Find the angle measure x in the given Figure
Find x + y + z
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram .
Find the measure of all the angles of a parallelogram, if one angle is 24° less than twice the smallest angle
If PQRS is a square, then write the measure of ∠SRP.
If the degree measures of the angles of quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and largest angle?
Can all the angles of a quadrilateral be right angles? Give reason for your answer.
One angle of a quadrilateral is of 108º and the remaining three angles are equal. Find each of the three equal angles.
A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is ______.
The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a ______.
