MCQ
In figure, if $\text{AE}||\text{DC}$ and $AB = AC$, the value of $\angle\text{ABD}$ is:
- ✓$110^\circ$
- B$120^\circ$
- C$70^\circ$
- D$130^\circ$
✓
Answer
Correct option: A.
$110^\circ$
$\angle\text{EAP} = \angle\text{BCA}$ (Corresponding angles)
$\angle\text{BCA} = 70^\circ$
$\angle\text{CBA} = \angle\text{BCA}$ (Angles opposite to equal sides are equal)
$\angle\text{CBA} = 70^\circ$
Now,
$\angle\text{ABD} + \angle\text{CBA }= 180^\circ$
$\angle\text{ABD} + 70 = 180^\circ$
$\angle\text{ABD} = 110^\circ$
$\angle\text{BCA} = 70^\circ$
$\angle\text{CBA} = \angle\text{BCA}$ (Angles opposite to equal sides are equal)
$\angle\text{CBA} = 70^\circ$
Now,
$\angle\text{ABD} + \angle\text{CBA }= 180^\circ$
$\angle\text{ABD} + 70 = 180^\circ$
$\angle\text{ABD} = 110^\circ$
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