Question

For the following figure, if $\mathrm{\Delta }AOD$is isosceles right triangle with right $\angle AOD$then the measure of$\angle A$is __?

Short answer

Then the measure is$\angle A\cong \angle D$.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of isosceles triangle.

Property of isosceles triangle states that if two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

Step 3. Step description.

From the figure $\overline{OA}=\overline{OD}$.

Here the angle opposite to side $\overline{OA}$is $\angle D$and the angle opposite to side $\overline{OD}$is $\angle A$in $\mathrm{\Delta }AOD$.

Since if the two sides of a triangle are congruent then the angles opposite to those sides are congruent then $\angle A\cong \angle D$.

Therefore, the congruent angles are $\angle A\cong \angle D$.