Angle Geometry: The Open Book
Consider a book that is opened completely flat.
The two halves of the book (the front cover/pages and the back cover/pages) lie on the same plane, extending outwards from the spine.
The angle formed at the spine, between these two halves, represents a straight line.
Angle Definition
A straight angle is defined as an angle measuring exactly 180 degrees ($180^\circ$). It forms a straight line.
Given that a fully open book forms a straight line at its spine:
- A right angle is $90^\circ$.
- A straight angle is $180^\circ$.
- An obtuse angle is greater than $90^\circ$ and less than $180^\circ$.
- An acute angle is less than $90^\circ$.
Therefore, the theoretical angle formed by the pages of a fully open book is a straight angle.
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:
- 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.
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?
