Question

in circle o, ad and be are diameters. what is mae? (0.5x + 34)° (3x)° 106° 138° 164° 132°

Explanation:

Step1: Use angle - sum property of a circle

The sum of the central angles in a circle is 360°. We know that one of the angles is 90° (the right - angle formed by the diameters), and the other two angles are (0.5x + 34)° and (3x)°. So, 90+(0.5x + 34)+3x=360.

Step2: Combine like terms

Combine the x - terms and the constant terms: 90 + 34+0.5x+3x=360, which simplifies to 124 + 3.5x=360.

Step3: Solve for x

Subtract 124 from both sides: 3.5x=360 - 124, so 3.5x=236. Then divide both sides by 3.5, x = \frac{236}{3.5}=\frac{2360}{35}=\frac{472}{7}\approx67.43.

Step4: Find the measure of the arc AE

The measure of arc AE is equal to the measure of its central angle ∠AOE. The central angle ∠AOE=90 + 3x. Substitute x=\frac{472}{7} into 3x, 3x = 3×\frac{472}{7}=\frac{1416}{7}\approx202.29. Then ∠AOE=90+\frac{1416}{7}=\frac{630 + 1416}{7}=\frac{2046}{7}=164.

Answer:

164°