Circle O is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is d, and the second arc formed is b. Arcs a and c are the other 2 arcs outside of the secants.
Which equation is correct regarding the measure of ∠1?

m∠1 = One-half(a – c)
m∠1 = One-half(a + c)
m∠1 = One-half(b – d)
m∠1 = One-half(b + d)

Circle O is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is d, and the second arc formed is b. Arcs a and c are the other 2 arcs outside of the secants.

Which equation is correct regarding the measure of ∠1?

m∠1 = One-half(a – c)

m∠1 = One-half(a + c)

m∠1 = One-half(b – d)

m∠1 = One-half(b + d)

abidemiokin abidemiokin · Answer 2 · 2022-03-16T10:57:55+01:00

The equation is correct regarding the measure of ∠1 is

m<1 = 1/2(arc b - arc d)

Circle geometry

Using the theorem that states that angle at the vertex is equal to half of the difference of its intercepted arcs.

Given the following parameters

m<1

arc A

arc B

Differnce of interceptd arcs = (arc b - arc d)

m<1 = 1/2(arc b - arc d)

Hence the equation is correct regarding the measure of ∠1 is

m<1 = 1/2(arc b - arc d)

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