Exterior Angle of a Triangle = Sum of Opposite Internal Angles

Q.

Find the measures of the angle marked by the letters in the following diagram,

Q. The internal bisector of angle $A$ in a triangle $ABC$ with $AC>AB$, meets the circumcircle $\Gamma$ of the triangle in $D$. Join $D$ to the centre $O$ of the cirlce $\Gamma$ suppose $DO$ meets $AC$ in $E$, possibly when extended. Given that $BE$ is perpendicular to $AD$, show that $AO$ is parallel to $BD$.

Q. Prove: Angles opposite to equal sides of an isosceles triangle are equal.

Q. If $\angle P={52}^o$ and $\angle PQO={64}^o$. If $QO$ and $RO$ are bisectors of $\angle PQR$ and $\angle PRQ$ respectively, then the value of $\angle x$ and exists but value of $\angle y$ does not exists

1. True
2. False

Q.

In the given triangle, $\angle 4$= $\angle 3+$_________.

Q. In the figure given 'O' is the centre of the circle. If QR$=$OP and $\angle$ORP$={20}^o$. Find the value of 'x' giving reasons.

Q. In the figure, PQ = RS and $\angle ORS={48}^o$. Find $\angle OPQ$ and $\angle ROS$.