Question
Arlo wants to prove that opposite angles of quadrilaterals inscribed in circles are supplementary. They consider quadrilateral
G
T
R
Y
inscribed in circle
M
. They want to prove that
∠
R
and
∠
G
are supplementary. Which of the following should they use as their proof? (1 point)
Responses
Together, the intercepted arcs of
∠
R
and
∠
G
create circle
M
, which measures 360°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of
∠
R
and
∠
G
is 180°. Therefore,
∠
R
and
∠
G
are supplementary.
Together, the intercepted arcs of angle upper R and angle upper G create circle upper M , which measures 360°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of angle upper R and angle upper G is 180°. Therefore, angle upper R and angle upper G are supplementary.
Together, the intercepted arcs of
∠
R
and
∠
G
create circle
M
, which measures 180°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of
∠
R
and
∠
G
is 90°. Therefore,
∠
R
and
∠
G
are supplementary.
Together, the intercepted arcs of angle upper R and angle upper G create circle upper M , which measures 180°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of angle upper R and angle upper G is 90°. Therefore, angle upper R and angle upper G are supplementary.
Together, the intercepted arcs of
∠
R
and
∠
G
create circle
M
, which measures 360°. Inscribed angles are equal to the measures of their intercepted arcs, so the sum of the measures of
∠
R
and
∠
G
is 360°. Therefore,
∠
R
and
∠
G
are supplementary.
Together, the intercepted arcs of angle upper R and angle upper G create circle upper M , which measures 360°. Inscribed angles are equal to the measures of their intercepted arcs, so the sum of the measures of angle upper R and angle upper G is 360°. Therefore, angle upper R and angle upper G are supplementary.
Together, the intercepted arcs of
∠
R
and
∠
G
create circle
M
, which measures 180°. Inscribed angles are equal to the measures of their intercepted arcs, so the sum of the measures of
∠
R
and
∠
G
is 180°. Therefore,
∠
R
and
∠
G
are supplementary.
G
T
R
Y
inscribed in circle
M
. They want to prove that
∠
R
and
∠
G
are supplementary. Which of the following should they use as their proof? (1 point)
Responses
Together, the intercepted arcs of
∠
R
and
∠
G
create circle
M
, which measures 360°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of
∠
R
and
∠
G
is 180°. Therefore,
∠
R
and
∠
G
are supplementary.
Together, the intercepted arcs of angle upper R and angle upper G create circle upper M , which measures 360°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of angle upper R and angle upper G is 180°. Therefore, angle upper R and angle upper G are supplementary.
Together, the intercepted arcs of
∠
R
and
∠
G
create circle
M
, which measures 180°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of
∠
R
and
∠
G
is 90°. Therefore,
∠
R
and
∠
G
are supplementary.
Together, the intercepted arcs of angle upper R and angle upper G create circle upper M , which measures 180°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of angle upper R and angle upper G is 90°. Therefore, angle upper R and angle upper G are supplementary.
Together, the intercepted arcs of
∠
R
and
∠
G
create circle
M
, which measures 360°. Inscribed angles are equal to the measures of their intercepted arcs, so the sum of the measures of
∠
R
and
∠
G
is 360°. Therefore,
∠
R
and
∠
G
are supplementary.
Together, the intercepted arcs of angle upper R and angle upper G create circle upper M , which measures 360°. Inscribed angles are equal to the measures of their intercepted arcs, so the sum of the measures of angle upper R and angle upper G is 360°. Therefore, angle upper R and angle upper G are supplementary.
Together, the intercepted arcs of
∠
R
and
∠
G
create circle
M
, which measures 180°. Inscribed angles are equal to the measures of their intercepted arcs, so the sum of the measures of
∠
R
and
∠
G
is 180°. Therefore,
∠
R
and
∠
G
are supplementary.
Answers
GPT-4o mini
The correct proof that Arlo should use to show that ∠R and ∠G are supplementary is:
**Together, the intercepted arcs of ∠R and ∠G create circle M, which measures 360°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of ∠R and ∠G is 180°. Therefore, ∠R and ∠G are supplementary.**
This option is correct because it accurately refers to the property of inscribed angles, which states that each inscribed angle is half the measure of its intercepted arc. Since ∠R and ∠G intercept arcs that, together, span 360°, the measures of ∠R and ∠G sum to 180°, thus proving that they are supplementary.
**Together, the intercepted arcs of ∠R and ∠G create circle M, which measures 360°. Inscribed angles are half the measures of their intercepted arcs, so the sum of the measures of ∠R and ∠G is 180°. Therefore, ∠R and ∠G are supplementary.**
This option is correct because it accurately refers to the property of inscribed angles, which states that each inscribed angle is half the measure of its intercepted arc. Since ∠R and ∠G intercept arcs that, together, span 360°, the measures of ∠R and ∠G sum to 180°, thus proving that they are supplementary.