Angle Sum Property of a Triangle

In the adjacent figure, $\angle BAC=2x+30°, \angle ABC=3x-40°$ and $\angle ACD=120°$. find the value of $x.$

Each of the two equal angles of a triangle is twice the third angle. Find the angles of the triangle.

In, $△ABC$, if $AB$ is the greatest side, then prove that $\angle C>{60}^o$.

The side $\mathrm{QR}$ of $△\mathrm{PQR}$ is produced on both sides to points $\mathrm{A}$ and $\mathrm{B}$ as shown in the figure. Prove that $\angle PQA+\angle PRB-180°=\angle QPR$.

In the given figure:

If $\angle 1= 2\angle 2$. Find $\angle 1, \angle 2 \text{and }\angle 3$

Find the lettered angles in the given figure:

What is the value of $x$ and $y$ in the given figure.

What is the value of $x$ and $y$ in the given figure.

In the given figure, $\angle \mathrm{BAC}=40°$. If $a:b=2:3$ and $c:d=2:3$, then $\angle \mathrm{BDC}$ equals

$\text{ If }PR\Vert QS\text{, find the measures of }x,y\text{ and }z\text{. }$

If$y=50°$ and $z=85°$, then $x$ in degrees is:

If the sum of two equal angles of a triangle is one third of third angle find all angles.

In the given figure, measure of $\angle BOC$ is 

In $△ABC$, $\angle BAC={90}^{°}$ and$AD\perp$$BC$. If $\angle BAD=40°$, then what is the numerical value of $\angle ACD$?

In the adjoining figure, $\mathrm{O}$ is the centre of the circle and $\mathrm{AB}$ is a tangent to it at point $\mathrm{B} \text{and} \angle \mathrm{BDC} = 65°.$ If$\angle \mathrm{BAO}=k°$,then find value of $k$

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In the given figure, $\mathrm{AB}$ is the diameter of the circle with centre $\mathrm{O},$ and $\mathrm{AT}$ is the tangent. Calculate the numerical value of $x$.

In the given figure,$\mathrm{ABCD}$ is a cyclic quadrilateral, $\mathrm{PQ}$ is tangent to the circle at point $\mathrm{C}$ and $\mathrm{BD}$ is its diameter. If $\angle \mathrm{DCQ}=40°$ and $\angle \mathrm{ABD}=60°,$ find $\angle \mathrm{ADB}$.

If $\mathrm{PQ}$ is a tangent to the circle at $\mathrm{R},$ calculate $\angle \mathrm{ROT}.$ Given that, $\mathrm{O}$ is the centre of the circle and angle $\mathrm{TRQ} = 30°.$

EDC is a triangle formed in this image. What is the value of angle q ?