Question

Can someone help I don't get it!!!! Solve for T. Type your answer in the blank without "T="

Answer 1

so let's recall that a full circle has a total of 360°, and we also know that these two arcs are on 3 : 1 ratio.

Now, let's notice the points A and E, the line AE passes through the center of the circle, that means the arc made by ABCE is half the circle or 180°.

So if we just divide 180 by (3 + 1) and then distribute accordingly to each arc, we'll see how many degrees each arc really has

`\stackrel{\widehat{ABC}}{3}~~ : ~~\stackrel{\widehat{CDE}}{1}\qquad \implies \qquad \stackrel{\widehat{ABC}}{3\cdot (180)/(3+1)}~~ : ~~\stackrel{\widehat{CDE}}{1\cdot (180)/(3+1)} \\\\\\ \stackrel{\widehat{ABC}}{3\cdot 45}~~ : ~~\stackrel{\widehat{CDE}}{1\cdot 45}\qquad \implies \qquad\stackrel{\widehat{ABC}}{135}~~ : ~~\stackrel{\widehat{CDE}}{45}`

Check the picture below.

Answer 2

45

Explanation:

arcAE = 180

arcABC : arcCDE = 3:1

ABC:CDE = 135:45

∠T = 1/2(135 - 45) = 45

Use the Far Arc -- Near Arc Formula: m∠T = 1/2(far-arc - near-arc) = 1/2(arcABC -arcCDE)