Angle Measure Fundamentals
An angle is formed by two rays (called arms) sharing a common endpoint, the vertex. The measure of the angle quantifies the amount of rotation between these two rays.
Impact of Extending Angle Arms
Consider an angle $\theta$. Its measure is determined solely by the relative orientation of its two arms originating from the vertex.
- Extending the length of an arm means making the ray longer, starting from the vertex.
- This extension does not alter the direction or inclination of the ray itself.
- Since the relative orientation between the two arms remains unchanged, the angle's measure ($\theta$) is unaffected.
Therefore, even if an arm of an angle is extended to double its length, the measure of the angle remains the same.
Correct Answer: Option 4, remains the same.
Similar Questions
- The measure of an angle is one half of its supplementary angle. Find its measure.
- The sum of two angles is $155^\circ$ and their difference is $\frac{\pi}{2}$. The value of the greater angle (in radians) is:
- The measure of an angle is three times the measure of its complement. The angles are respectively:
- 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 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 $125^\circ$?
- 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:
In the given figure, the three parallel lines are cut through by a transversal. Of the marked angles, the greater two are of equal measure. The ratio of a greater angle to the smaller angle is 7 : 3. What is the measure of the greater angle?
Important Questions from Lines and Angles
There are three points P, Q and R on a straight line such that PQ : QR = 3 : 5. If n is the number of possible values of PQ : PR, then what is n equal to ?
Two cars start from a point at the same time and travel on two different roads at right angles to each other. Their speed is 18 km/h and 72 km/h respectively. What will be the distance between them after 6 seconds?
Express 65° in radian :
The measure of an angle for which the measure of the supplement is four times the measure of the complement is:
AB||CD and EF is the transversal meeting AB and CD at P and Q, respectively. If ∠APE = 6x and ∠PQD = 4x, then ∠APQ =______.
