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ACT 1 Geo: Recognize relationships between lines

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ACT 1 Geo: Recognize relationships between lines

Welcome to your ACT 1 Geo: Recognize relationships between lines

$Q_{1}:$ The sum of the measures of the interior angles of an n-sided polygon is

$180(n-2)$

$90(n-2)$

$180(n-1)$

$90(n-1)$

$Q_{2}:$ The figure below is an equilateral inscribed in a circle with radius $10$. What is the measure of $\angle AOC $?

$120$

$108$

$60$

$50$

$Q_{3}:$ The figure below is an equilateral inscribed in a circle with radius $10$. What is the length of $OD$?

$2.5$

$10$

$5$

$8$

$Q_{4}:$ The figure below is an equilateral inscribed in a circle with radius $10$. What is the length of $BD$?

$15$

$10$

$5$

$1$

$Q_{5}:$ The figure below is an equilateral inscribed in a circle with radius $10$. What is the area of $\Delta ABC$?

$45\sqrt{3}$

$50\sqrt{3}$

$60\sqrt{3}$

$75\sqrt{3}$

$Q_{6}:$ The figure below is a regular pentagon whose radius is $6$. What is the value of $x $?

$108$

$46$

$112$

$120$

$Q_{7}:$ The figure below is a regular pentagon whose radius is $6$. What is the measure of $\angle RQS $?

$26$

$36$

$46$

$56$

$Q_{8}:$ The figure below is a regular pentagon whose radius is $6$. Which of the following equations can be used to find the value of $a $?

$sin \angle RQS =\frac{a}{6} $

$cos \angle RQS =\frac{a}{6} $

$sin \angle RQS =\frac{6}{a}$

$cos \angle RQS =\frac{6}{a}$

$Q_{9}:$ A chord is

an angle.

is a line in the plane of a circle, and intersects

a segment whose endpoints lie on a circle.

is a line in the plane of a circle, and intersects the circle at exactly one point.

$Q_{10}:$ which of the following is a point tangency?

$P$

$Q$

$R$

$Q_{11}:$ Which of the following is a minor arcs?

$PQ$

$QR$

$RS$

All of the above

$Q_{12}:$ In the figure below, $O$ is inscribed in $\Delta PQR $. If $PA = 12 , QA = 6 $, and $RB = 9.5 $, what is the perimeter of $\Delta PQR $?

$46$

$49$

$52$

$55$

$Q_{13}:$ In the figure below, $AB$ is an arc of a circle with radius $27 $cm. If the length of arc $AB$ is $k\pi $ , what is the value of $k $?

$6$

$7$

$3$

$4$

$Q_{14}:$ In the figure below, $AB$ is an arc of a circle with radius $27 $cm. If the area of sector $OAB$ is $n\pi $ , what is the value of $n $?

$60$

$70$

$81$

$90$

$Q_{15}:$ The figure below shows arcs of length $8, 7, 6, 5, $ and $4$. If m $AB = 120 $, what is the degree measure of angle $a $?

$30$

$32$

$40$

$20$

$Q_{16}:$ In the figure below, the radius of the circle is $8$ and m$ \angle AOB = 120$. What is the length of $\overline{AB }$?

$8\sqrt{2}$

$8\sqrt{3}$

$12\sqrt{2}$

$12\sqrt{3}$

$Q_{17}:$ In the figure below, $OP= OQ$ and $\overline{PQ}$ is tangent to circle $O $. If the radius of circle $O$ is $8$, what is the length of $\overline{QR }$?

$10(\sqrt{2}-1)$

$6$

$10(\sqrt{3}-1)$

$8$

$Q_{18}:$ ................ is an angle whose vertex is on a circle and whose sides contain chords of the circle.

A central angle

A center angle

An inscribed angle

An interior angle

$Q_{19}:$ In the figure below, the values of $x$ and $y$ is

$32$

$64$

$30$

none

$Q_{20}:$ In the figure below, $AC$ is a diameter and m $AB = 72 $. The values of a , b , and c are?

$a=90$, $b= 54$, $c= 36$

$a=54$, $b= 36$, $c= 90$

$a=54$, $b= 90$, $c= 36$

$a=36$, $b= 90$, $c= 54$

$Q_{21}:$ Find the values of $p$ and $q$?

$p=180$, $q=86$

$p=86$, $q=180$

$p=100$, $q=76$

$p=76$, $q=100$

$Q_{22}:$ What is the value of $y $?

$30$

$100$

$84$

$48$

$Q_{23}:$ What is the value of $x$?

$24$

$30$

$21$

$48$

$Q_{24}:$ What is the value of $w$?

$50$

$90$

$12$

$30$

$Q_{25}:$ The figure below shows a semicircle with the lengths of the adjacent arcs $a, a +1, a + 2, a + 3,$ and $a + 4 $. If the value of $x$ is $42$, what is the value of $a $?