Question

Match the values of $x$ for the following, given that triangles ABC are isosceles triangles with AB=AC.

• A. ${80}^{\circ }$
• B. ${70}^{\circ }$
• C. 10cm

Answer 1

We know that:
In an isosceles $\Delta$, base angles are equal.
Also the sum of interior angles of a $\Delta$ is ${180}^{\circ }$
1.
Hence
$\angle C={50}^{\circ }\to \angle A={180}^{\circ }-({50}^{\circ }+{50}^{\circ })={80}^{\circ }$
2.
$\angle B=\frac{180-40}{2}={70}^{\circ }$

3.
As AB=AC and AO$\perp$ BC $\to$ BO=OC =6cm
$AC=$10cm ( 6,8,10 forms a Pythagorian triplet)

We can also verify the same:
$A{O}^2+O{C}^2=A{C}^2$
=$8^2+6^2=A{C}^2=64+36=100$
Hence AC = 10