Question

A,B,C,D are four points on the circumference of a circle .AEC and BED are straight lines. sate with a reason which other angles is is equal to abd

Answer 1

Answer: ABD is equal to angle AEC.

Explanation:

If A, B, C, and D are four points on the circumference of a circle and AEC and BED are straight lines, then we can conclude that angle ABD is equal to angle AEC.

This is because of the Inscribed Angle Theorem, which states that an angle formed by two chords in a circle is half the sum of the arc lengths intercepted by the angle and its vertical angle. In this case, angle ABD is formed by the chords AB and BD, and angle AEC is formed by the chords AC and CE. The arc lengths intercepted by these angles are arc AD and arc AC, respectively. Since arc AD and arc AC are congruent arcs (they both intercept the same central angle), angles ABD and AEC must be congruent by the Inscribed Angle Theorem.

Answer 2

a) Angle ABD is equal to angle CBE because they are vertically opposite angles.

b) Angle AEB is equal to the sum of angles ABC and CBE due to the Exterior Angle Theorem.

c) If angle ABC is 88°, angle ADC is also 88° as it is the sum of angles ABC and BCD according to the Exterior Angle Theorem.

a) Angle ABD is vertically opposite to angle CBE. Vertically opposite angles are equal. Therefore, angle ABD is equal to angle CBE.

b) Angle AEB is an exterior angle to triangle BEC. According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Thus, angle AEB is equal to the sum of angles ABC and CBE.

c) Angle ADC is an exterior angle to triangle ABC. By the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Therefore, angle ADC is equal to the sum of angles ABC and BCD.