Question

Arlo wants to prove that opposite angles of quadrilaterals inscribed in circles are supplementary. They consider quadrilateral GTRY
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 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.
Together, the intercepted arcs of angle upper R and angle upper G create circle upper M , which measures 180°. 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 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 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.

Answer 1

"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 is correct because each inscribed angle equals half its intercepted arc; the two opposite intercepted arcs sum to 360°, so the angles sum to 1/2·360° = 180°.