Special Angles

The external bisector of $\angle \mathrm{ABC}$ in $△\mathrm{ABC}$ intersects the straight line through A and parallel to $\mathrm{BC}$ at the point D. If $\angle \mathrm{ABC} =50°$  then measure of $\angle \mathrm{ADB}$ is equal to_______.

In the following fig, FD and AE are parallel to each other and $\angle ABC={49}^0$, then $\angle ABC+\angle DCB$ is equal to

In the figure given, $BD\parallel AE$. If $\overline{CE}=3 \mathrm{cm}$, what is the length of $\overline{AC}$?

Consider the following statements regarding vertically opposite angle:

$\left(i\right)$. Vertically opposite angles share a common point.

$\left(ii\right)$. The point which is a common vertex of two vertically angles is also called the point of concurrency

$\left(iii\right)$. Vertical angles are a pair of adjacent angles 

Which of the above statements is/ are not correct?

Which of the following statements is/are true for vertically opposite angles:

$\left(i\right)$Vertical angles are always equal.

$\left(ii\right)$Vertical angles can be supplementary as well as complimentary.

$\left(iii\right)$Vertical angles are always adjacent.

If lines $PQ$ and $RS$ intersect at point $T$, such that $\angle PRT=39°, \angle RPT=71°$ and $\angle TSQ=55°$. Find $\angle SQT$.

In the figure, what is the value of $\left(4x+20\right)$?

Find the measurement of the angles from the given figure,

Here, $\angle 2=135°$. Find the value of $\angle 4$.

Refer to the figure. Fill in the blank.

$\angle 2$ and _____ are vertical angles.

Find the measurement of the angles from the given figure,

Here, $\angle 1=35°$. Find the value of $\angle 4$.

In the given figure, if $QP\parallel SR$, then the value of $a$ is

In the given figure, $a$ and $b$ are

In the given figure, $PQ\mathit{\parallel }SR$ and $SP\mathit{\parallel }RQ$. Then, angles $a$ and $b$ are respectively

In the given figure, $PA\parallel BC\parallel DT$ and $AB\parallel DC$. Then, the values of $a$ and $b$ are respectively.

In the given figure, if $AB\parallel CD, \angle APQ=50°$ and $\angle PRD=130°$, then $\angle QPR$ is

In the given figure, $\overline{CD}\parallel \overline{EF}$. The alternate interior angle to $\angle CMN$ is

$AB$ and $CD$ are parallel lines cut by the transversal $t$. Find the unknown angle marked $x$ in the following diagram.

In the given figure, $\mathrm{AB} \parallel \mathrm{DE}$.
Find $\angle \mathrm{x}$.

If two lines intersect, the vertically opposite angle are

In the below figure, what is the value of $3x$?