Complementary Angles Definition
Two angles are complementary if the sum of their measures is exactly $90^\circ$.
Setting Up the Equation
Let the measure of one angle be $x$. Since the angles are complementary, the measure of the other angle is $90^\circ - x$.
The problem states that the measure of an angle is three times the measure of its complement. We can write this relationship as an equation:
$x = 3 \times (90^\circ - x)$
Solving for the Angle Measure
- Distribute the 3 on the right side of the equation:
$x = 270^\circ - 3x$ - Add $3x$ to both sides to gather the $x$ terms:
$x + 3x = 270^\circ$
$4x = 270^\circ$ - Divide by 4 to solve for $x$:
$x = \frac{270^\circ}{4}$
$x = 67.5^\circ$
Finding Both Angles
We found one angle to be $x = 67.5^\circ$.
The measure of its complement is $90^\circ - x = 90^\circ - 67.5^\circ = 22.5^\circ$.
So, the two angles are $22.5^\circ$ and $67.5^\circ$.
We can check: Is $67.5^\circ$ three times $22.5^\circ$? Yes, $3 \times 22.5^\circ = 67.5^\circ$.
This matches option B.
Similar Questions
- The supplement of $70^\circ$ is:
- The cost price of 120 g of rice is the same as the selling price of 150 g of it. The percentage loss is:
- Which native Indian dynasty issued their own coins with portraits of their rulers on them?
- The sum of two angles is $155^\circ$ and their difference is $\frac{\pi}{2}$. The value of the greater angle (in radians) is:
- Two adjacent angles form an angle of $100^{\circ}$. The larger angle is $20^{\circ}$ less than five times the smaller angle. The larger angle is:
- When an arm of an angle is extended to double its length, then the measure of the angle:
- The measure of an angle is one half of its supplementary angle. Find its measure.
- The angle formed by the pages of a fully open book, with just few pages, is theoretically:
What is the sum of the angle complementary to $15^\circ$ and the angle supplementary to $125^\circ$?
In the given figure, AB and CD are parallel lines. O is a point such that angle CDO = $70^\circ$ and angle DOB = $100^\circ$. Find angle ABO.
Important Questions from Lines and Angles
If angles of a triangle are in the ration of 2 : 3 : 4, then the measure of the smallest angle is:
In the triangle, if AB = AC and ∠ABC = 72°, then ∠BAC is:
The angles of a triangle are (8x - 15)°,(6x - 11)° and ( 4x – 10)°. What is the value of x ?
In a ΔABC, the bisectors of ∠B and ∠C meet at point O, inside the triangle. If ∠BOC = 122°, then the measure of ∠A is:
In ΔABC, D is a point on side BC such that ∠ADC = 2∠BAD. If ∠A = 80° and ∠C = 38°, then what is the measure of ∠ADB?
