Answer: A) 35°
Step-by-step explanation:
In the given picture , we have an isosceles triangle , in which h is an angle bisector , divide an angle into two parts named as ∠a and ∠a.
∠c = 55°
We know that the angles opposite to the equal sides of an isosceles triangle are equal.
[tex]\Rightarrow\ \angle{b}=\angle{c}=55^{\circ}[/tex]
By angle sum property , we have
[tex]\angle{a}+\angle{a}+\angle{b}+\angle{c}=180^{\circ}[/tex]
[tex]\Rightarrow\ 2\angle{a}+55^{\circ}+55^{\circ}=180^{\circ}[/tex]
[tex]\Rightarrow\ 2\angle{a}=180^{\circ}-110^{\circ}[/tex]
[tex]\Rightarrow\ 2\angle{a}=70^{\circ}[/tex]
[tex]\Rightarrow\ \angle{a}=35^{\circ}[/tex] [Divide both sides by 2]
Hence, the correct answer is A) 35° .
