Question

In figure, sides AB and AD of a quadrilateral ABCD are produced to E and F respectively. If ∠CBE = 100°, then find ∠CDF.


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Answer 1

Hey Mate,

Here's your answer,

___________________

(It is a complicated answer, Read it carefully!)

=> As we know <CBE = 100°

=> So,

=> Angle <DCB = 100° ( Acute angle property)

=> So,

=> Angle <CDF = 100° ( Acute angle property)

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$hope \: it \: helps$

Answer 2

Answer: ∠CDF = 100°

Given:

• ∠CBE = 100°
• Sides AB and AD of a quadrilateral ABCD are produced to E and F.

To Find: ∠CDF

Step-by-step explanation:

Step 1: According to the definition, a cyclic quadrilateral is a quadrilateral that is encircled by a circle. This indicates that the quadrilateral's four vertices are located within the circle's circumference.

Let ∠A, ∠B, ∠C and ∠D are the four angles of an inscribed quadrilateral. Then,

∠A + ∠C = 180°

∠B + ∠D = 180°

Step 2: A straight angle is an angle equal to 180 degrees. Thus

As given,

∠CBE = 100°

∠CBA + ∠CBE = 100° (Straight angle)

∠CBA = 180°- 100° = 80°

∠CBA + ∠ADC = 180° (Cyclic quadrilateral property)

∠ADC = 180° - 100° = 80°

∠ADC + ∠CDF = 180° (Straight angle)

∠CDF = 180° - 80° = 100°

Hence, ∠CDF = 100° is the correct answer.

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