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Circle — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsCircle1 Mark
Question
In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that $\angle\text{ADC}=95^\circ$ and $\angle\text{ECF}=20^\circ.$ Then, $\angle\text{EAD}=?$

  1. 95°
  2. 85°
  3. 105°
  4. 75°

✓

Answer

  1. 105°

Solution:

Since CF || AB, $\angle\text{ABC}=\angle\text{BCF}=85^\circ$

$\angle\text{BAD}=\angle\text{BCE}$

$\Rightarrow\ \angle\text{BAD}=\angle\text{BCF}+\angle\text{ECF}$

$\Rightarrow\ \angle\text{BAD}=105^\circ$

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