3cm×10cmstart color #1fab54, 3, start text, c, m, end text, times, 10, start text, c, m, end text, end color #1fab54 rectangle sits inside a circle with radius of
12
cm
12cmstart color #11accd, 12, start text, c, m, end text, end color #11accd.
Why? The triangle in the problem is an isosceles triangle. That means the two legs of the triangle are equal and the angle opposite to the equal legs are also equal. Therefore, angle C is also 74°. The sum of the interior angles of a triangle is equal to 180°. Thus, 180° = ∡A + ∡B + ∡C 180° = 74° + ∡B + 74° 180° = 148° + ∡B ∡B = 180° - 148° ∡B = 32°
We want to know the arc measure for the whole circle, except for DC. So, we can subtract the arc measure of DC from 360 to find DBC. Since we found DC above, all we need to do is subtract.