ACT 1 Geo: Use angle relationships to solve problems

Welcome to your ACT 1 Geo: Use angle relationships to solve problems

$Q1:$ If $C$ is in the interior of $\angle AOB$, then

$m\angle AOB= m\angle AOC + m\angle COB$

$m\angle AOB= 2 m\angle AOC $

$m\angle AOB= m\angle AOC - m\angle COB$

$m\angle AOB= m\angle COB + m\angle AOC $

$Q_{2}:$ In the figure shown, $m\angle POQ = 55 $. Find the $m\angle SOT$

$35$

$45$

$55$

$65$

$Q_{3}:$ In the figure shown, $m\angle POQ = 55 $. Find the $m\angle ROT$

$60$

$70$

$90$

$100$

$Q_{4}:$ In the figure below, what is the value of $x $?

$140$

$160$

$190$

$230$

$Q_{5}:$ In the figure, what is the values of $y$ ?

$52$

$60$

$68$

$76$

$Q_{6}:$ In the figure, ray $OB$ bisects $\angle COA $. If $m\angle DOB =11x+ 6$ and $m\angle COA =8x-12$, what is the measure of $\angle DOC $?

$92$

$96$

$102$

$108$

$Q_{7}:$ In the figure, $m\angle ABE = 120$ and $m\angle CBD = 135$. What is the measure of $\angle DBE $?

$63$

$68$

$75$

$79$

$Q_{8}:$ In the figure below, $l\parallel m$ , $r\perp t$ and $m\angle 1 =32 $. Lines $l , r ,$ and $t$ intersect at one point. Find $m\angle 2$ ?

$54$

$58$

$62$

$32$

$Q_{9}:$ In the figure below, $l\parallel m$ , $r\perp t$ and $m\angle 1 =32 $. Lines $l , r ,$ and $t$ intersect at one point. Find $m\angle 3$ ?

$54$

$58$

$62$

$32$

$Q_{10}:$ In the figure below, $l\parallel m$ , $r\perp t$ and $m\angle 1 =32 $. Lines $l , r ,$ and $t$ intersect at one point. Find $m\angle 4$ ?

$30$

$60$

$90$

$32$

$Q_{11}:$ In the figure below, $l\parallel m$ , $r\perp t$ and $m\angle 1 =32 $. Lines $l , r ,$ and $t$ intersect at one point. Find $m\angle 5$ ?

$30$

$60$

$90$

$32$

$Q_{12}:$ In the figure below, $r\parallel t$. What is the value of $x+y$?

$37$

$40$

$43$

$46$

$Q_{13}:$ In the figure below, $m\parallel n$. If $a = 50$ and $b = 120 $, what is the value of $c $?

$50$

$60$

$70$

$80$

$Q_{14}:$ In the figure, lines $l,m$, and $n$ are parallel. What is the value of $x+ y$?

$160$

$200$

$230$

$290$

$Q_{15}:$ In the figure below, $l\parallel m$. What is the value of $x $?

$30$

$35$

$40$

$45$

$Q_{16}:$ In the figure below, $l\parallel m$. What is the value of $x $?

$45$

$50$

$55$

$60$

$Q_{17}:$ In the figure below, $l\parallel m$. What is the value of $y$?

$120$

$125$

$130$

$135$

$Q_{18}:$ In the figure, lines $l$ and $m$ are parallel and $\overline{BD}$ bisects $\angle ABC$. What is the value of $x $?

$54$

$60$

$68$

$72$

$Q_{19}:$ In the figure below, $\overline{DA} \parallel \overline{BC}$ and $\overline{AB}$ bisects $\angle DAC $. What is the measure of $\angle BCA$ in terms of $a $?

$180-a$

$2a-180$

$180-2a$

$2a-90$

$Q_{20}:$ In the figure below, $\overline{AB} \parallel \overline{CD}$ and $\overline{BC} \parallel \overline{DE}$. What is the value of $x $?

$47$

$51$

$55$

$57$

$Q_{21}:$ In the figure below, $r \parallel t$. What is the value of $a+b$?

$160$

$175$

$185$

$200$

$Q_{22}:$ In the figure below, what is the value of $x+y$?

$540$

$520$

$500$

$480$

$Q_{23}:$ In the figure below, $\overline{PQ}$ is parallel to $\overline{ST }$. What is the measure of $\angle QRS $?

$120$

$115$

$105$

$100$

$Q_{24}:$ In $\Delta ABC$, if $AB= AD =DC$, what is the value of $x $?

$92$

$96$

$102$

$108$

$Q_{25}:$ In the figure below, $AD= BD =BC$. If $m\angle A = 26 $, what is the measure of $m\angle DBC $?

$68$

$72$

$76$

$82$

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