Angle Measure Calculation
Setting Up the Supplementary Angle Equation
Let the measure of the unknown angle be $x$.
Two angles are supplementary if their sum is $180^{\circ}$. Therefore, the supplementary angle to $x$ measures $180^{\circ} - x$.
The problem states that the measure of the angle ($x$) is one half of its supplementary angle ($180^{\circ} - x$). This can be written as an equation:
$x = \frac{1}{2} (180^{\circ} - x)$
Solving for the Angle
To find the measure of the angle, we solve the equation:
- Multiply both sides of the equation by 2 to eliminate the fraction:
$2 \times x = 2 \times \frac{1}{2} (180^{\circ} - x)$
$2x = 180^{\circ} - x$
- Add $x$ to both sides of the equation to gather the terms involving $x$ on one side:
$2x + x = 180^{\circ} - x + x$
$3x = 180^{\circ}$
- Divide both sides by 3 to isolate $x$:
$x = \frac{180^{\circ}}{3}$
$x = 60^{\circ}$
Thus, the measure of the angle is $60^{\circ}$.
Similar Questions
- The supplement of $70^\circ$ is:
- The measure of an angle is three times the measure of its complement. The angles are respectively:
- 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:
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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?
