Sam constructed ∠B
as a copy of ∠A
using a straightedge and compass. If the measure of ∠A
is 42 degrees, what is the measure of ∠B
?
(1 point)
The measure of the copy of the angle that Sam created is
degrees.
The measure of ∠B is also 42 degrees.
Elias measured an angle he was given to be 81 degrees. He constructed a copy of this angle using a compass and straightedge. What is the measure of the copy of the angle he constructed?(1 point)
The measure of the copy of the angle Elias created is
degree
The measure of the copy of the angle Elias created will also be 81 degrees.
Javier constructed ∠AOB
with ray OC
as an angle bisector of ∠AOB
. If the measure of ∠AOB
is 74 degrees, what is the measurement of ∠AOC
?
(1 point)
The m∠AOC
is
degrees.
Since OC is an angle bisector of ∠AOB, ∠AOC and ∠COB are congruent and each measure half of ∠AOB.
So, ∠AOC = ∠COB = 74/2 = 37 degrees.
Ines examined the triangle and noticed that segment AD
bisected ∠CAB
. She measured ∠BAD
to be 21 degrees. What is the measure of ∠CAB
in degrees?
(1 point)
The m∠CAB
is
degrees.
Since AD bisects ∠CAB, ∠BAD and ∠CAD are congruent.
Since ∠BAD measures 21 degrees, ∠CAD also measures 21 degrees.
Therefore, ∠CAB is the sum of ∠BAD and ∠CAD, which is 21 + 21 = 42 degrees.
On her paper, Katarzyna wants to construct the angle bisector of angle ∠PQR
. She has drawn an arc from the vertex point Q
that intersects both sides of the angle and has labeled the intersection of the arc with the sides of the angle with P
and R
. Using a compass and straightedge, what next step must she take to construct the angle bisector?
Option #1: Move the compass further apart and place the pointed end at point Q
and draw another arc that intersects the sides of the angle.
Option #2: Place the pointed end of the compass on point P
and draw another arc inside the first arc and between two sides of the angle.
Option #3: Place the pointed end of the compass on point P
and draw another arc outside the first arc and between two sides of the angle.
Option #4: Draw a line extending from the vertex point Q
through the middle of the angle.
(1 point)
Katarzyna’s next step is Option #
.
Katarzyna's next step is Option #2: Place the pointed end of the compass on point P and draw another arc inside the first arc and between two sides of the angle.
To copy ∠A using a straightedge and compass, Sam needs to follow these steps:
1. Place the compass point on the vertex of ∠A and draw an arc that intersects both sides of the angle.
2. Without changing the compass width, place the compass point on the intersection points of the first arc and each side of ∠A.
3. Draw two arcs inside ∠A that intersect each other.
4. Using the straightedge, draw a line connecting the vertex of ∠A to the intersection point of the two arcs.
5. The angle formed by the line and one of the sides of ∠A will be the copy of ∠A, which we'll call ∠B.
Now that we have copied ∠A to ∠B, we can determine the measure of ∠B. Since ∠A measures 42 degrees, ∠B will also measure 42 degrees because they are congruent angles.
Therefore, the measure of the copy of the angle that Sam created, ∠B, is 42 degrees.