Question

In the given figure, mBC =118°, mBE=76°, and m

a.) the measure of DE is 48°, and triangle BCD is isosceles.

b.) the measure of DE is 83°, and triangle BCD is isosceles

c.) the measure of DE is 48°, and triangle BCD is not isosceles.

d.) the measure of DE is 83°, and triangle BCD is not isosceles.

Answer 1

Correct option: A

Explanation:

The angle BDC inscribe the arc mBC, so we have that:

mBDC = (1/2) * mBC

mBDC = (1/2) * 118 = 59°

From the secants relation in a circle, we have that:

mA = (1/2) * (mBC - mDE)

35 = (1/2) * (118 - mDE)

70 = 118 - mDE

mDE = 48°

The sum of the arcs is 360°, so we have:

mBC + mCD + mDE + mBE = 360

118 + mCD + 48 + 76 = 360

mCD = 360 - 118 - 48 - 76 = 118°

The angle mCBD inscribes the arc mCD, so we have:

mCBD = (1/2) * mCD = (1/2) * 118 = 59°

The angles mCBD and mBDC are equal, so the triangle is isosceles.

Correct option: A