ACT 1 Geo: Relate interior and exterior angles

$Q_{1}:$ The measure of each interior angle of a regular n-sided polygon is

$Q_{2}:$ The sum of the measures of the interior angles of an n-sided polygon is

$Q_{3}:$ In $\Delta ABC$ shown below, $AB= BC$, $m\angle BCD = 110$ and $m\angle BDE= 140$. Find $m\angle 1$?

$Q_{4}:$ In $\Delta ABC$ shown below, $AB= BC$, $m\angle BCD = 110$ and $m\angle BDE= 140$. Find $m\angle 2$?

$Q_{5}:$ In $\Delta ABC$ shown below, $AB= BC$, $m\angle BCD = 110$ and $m\angle BDE= 140$. Find $m\angle 3$?

$Q_{6}:$ In $\Delta ABC$ shown below, $AB= BC$, $m\angle BCD = 110$ and $m\angle BDE= 140$. Find $m\angle 4$?

$Q_{7}:$ In the triangle below, what is the value of $x $?

$Q_{8}:$ In $\Delta ABC$ below, if $AB= AD= DC$, what is the value of $x $?

$Q_{9}:$ In the figure below, $AC\perp BC$. What is the measure of $\angle ABC $?

$Q_{10}:$ In the figure below, $AD= BD =BC$. If $m\angle A = 26 $, what is the measure of $m\angle DBC $?

$Q_{11}:$ In the figure below, $\overline{PQ} \perp \overline{QR}$ and $\overline{PQ} \cong \overline{PT}$. What is the measure of $\angle R $?

$Q_{12}:$ In the figure below, what is the value of $a- b$?

$Q_{13}:$ A regular hexagon with the length of side of $4$ is shown at below. Find the $m\angle PQS$?

$Q_{14}:$ In triangle $ABC$, angle $A$ is three times as large as angle $B$. The exterior angle at $C$ is $100$. Find the number of degrees in angle $A$?

$Q_{15}:$ In triangle $ABC$, $\overline{AB} =\overline{ BC} $. If angle $A = (4x – 30)$ and angle $C = (2x + 10)$, find the number of degrees in angle $B$.

$Q_{16}:$ Find the number of degrees in the sum of the interior angles of a hexagon?

$Q_{17}:$ The sum of the angles in a rhombus is?

$Q_{18}:$ A conditional statement is given "If two interior angles of a triangle are acute, then the third interior angle must be obtuse". Which of the following best describes this statement?

$Q_{19}:$ What is the sum of $x$ and $y$ in degree?

$Q_{20}:$ In $\Delta ABC$, the measures of the exterior angles at vertices $A$ and $B$ are $145$ and $125$ , respectively. Which of the following statements about $\Delta ABC$ must be true?

$Q_{21}:$ What is the value of $w$ in the figure below?

$Q_{22}:$ What is the value of $a+b+c+d+e$ in the figure below?

$Q_{23}:$ How many sides does a polygon have if the measure of each interior angle is $9$ times the measure of each exterior angle?

$Q_{24}:$ If $ABD$ is a right isosceles triangle, then $x =$?

$Q_{25}:$ The measure of each angle in a regular decagon is?

$Q_{26}:$ Each of the following statements is true EXCEPT: