Since it's an inscribed angle, the measure of angle 1 is one-half the measure of intercepted arc AED.
But we need to first find the measure of minor arc AE, since it's not known.
This is given by subtracting all the other known arc measures from 360. So we have:
(360 - 84 - 38 - 64 - 60) = 114
And since m arc AED = m arc AE + m arc DE, we have
114 + 60 = 174
And 1/2 of this = 87 degrees = m angle 1.
Since it's an inscribed angle, the measure of angle 1 is one-half the measure of intercepted arc AED.
But we need to first find the measure of minor arc AE, since it's not known.
This is given by subtracting all the other known arc measures from 360. So we have:
(360 - 84 - 38 - 64 - 60) = 114
And since m arc AED = m arc AE + m arc DE, we have
114 + 60 = 174
And 1/2 of this = 87 degrees = m angle 1.