Triangle Angle Sum Property
A fundamental property in Euclidean geometry states that the sum of the interior angles of any triangle is always constant.
For any triangle, let the measures of the three interior angles be $\alpha$, $\beta$, and $\gamma$. The angle sum property states that:
$ \alpha + \beta + \gamma = 180^\circ $
Therefore, the total measure of angles in any triangle is $180^\circ$.
Similar Questions
- In $\triangle ABC$, $BD \perp AC$ at $D$ and $\angle DBC = 40^\circ$. $E$ is a point on $BC$ such that $\angle CAE = 37^\circ$. What is the measure of $\angle AEB$?
- In $\Delta PQR$, QR is extended up to S, so that RS = RP. If $\angle RPQ = 55^\circ$ and $\angle PRS = 110^\circ$, then find the measure of $\angle PQS$.
- In a triangle, if angle $A = 30^\circ$ and angle $B = 45^\circ$, then what is the angle of C?
- ABC is a triangle. BI and CI are angle bisectors of $\angle ABC$ and $\angle ACB$. $\angle BAC = 45^\circ$. Find the measure of $\angle BIC$.
- A side of the triangle is 15 cm and the height of the triangle from this side is 6 cm. Find the area of triangle.
- Area of an equilateral triangle is $49\sqrt{3}\text{ cm}^2$. Find the side of the triangle.
- In a triangle the ratio of angles is 2 : 3 : 4. Find the difference between the greatest and the smallest angle.
- The perimeter of an equilateral triangle is $36\sqrt{3}$ m. Find the height (in metres).
- Write a Pythagorean triplet whose smallest member is 8.
- The lengths of two sides of a triangle are 7 cm and 8 cm respectively and the measure of the angle included between these two sides is $60^\circ$. The length (in cm) of the third side of the triangle is:
Important Questions from Triangles
Among the following options, which are NOT sides of a triangle?
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
In the equilateral Δ ABC, the base BC is trisected at D and E. The line through D, Parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. If EG and DF intersect at H, then what is the ratio of the sum of the area of parallelogram AGHF and the area of the Δ DHE to the area of the Δ ABC?
The product of the perimeter of a triangle, the radius of its in‐circle, and a number gives the area of the triangle. The number is
A man goes 24 m towards east and then 10 m towards north. How far is he away from his initial position?
