Advertisements
Advertisements
Question
Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is
Options
45°
30°
36°
none of these
Advertisements
Solution
Let one angle be x°.
Then, the other complementary angle becomes (90 - x)°
It is given that two times the angle measuring x°is equal to three times the angle measuring (90 - x)°
Or, we can say that:
2x = 3(90 - x)
2x = 270 - 3x
2x + 3x = 270
5x = 270
On dividing both sides of the equation by 5,we get
`x = 270/5`
x = 54
Also, the other complementary angle becomes
90 - x = 90 - 54
= 36
Thus, the measure of the required smaller angle is 36°.
APPEARS IN
RELATED QUESTIONS
If an angle is 30° more than one half of its complement, find the measure of the angle.
Two straight lines AB and CD cut each other at O. If ∠BOD = 63°, then ∠BOC =
State, true or false:
A ray has one endpoint and a line segment has two end-points.
In the following figure, ∠AOB and ∠AOC are adjacent angles? Give the reason for your answer.
In the following figure, ∠AOB and ∠AOC are adjacent angles? Give the reason for your answer.
In the following figure, ∠AOB and ∠AOC are adjacent angles? Give the reason for your answer.
Write the complement of a°
Write the complement of `1/3` of 180°
In the given figure, lines PQ, MN, and RS intersect at O. If x : y = 1 : 2 and z = 90°, find ∠ROM and ∠POR.
In the given figure, find the measure of the unknown angles:
