Triangle ABC is an isosceles right triangle. What is the measure of a base angle?
Answer:
The measure of base angle is 45°
Step-by-step explanation:
Given that triangle ABC is an isosceles right triangle.
we have to find the measure of base angles.
As given triangle is right angled triangle therefore one angle which is not a base angle is of 90°
Also the triangle ABC is isosceles therefore two sides of triangle are equal and angles opposite to the equal sides are equal.
Let these equal angles which are base angles is x°
By angle sum property of triangle,
the sum of all angles of triangle equals to 180°
∠A+∠B+∠C=180°
[tex]x^{\circ}+90^{\circ}+x^{\circ}=180^{\circ}[/tex]
[tex]2x^{\circ}+90^{\circ}=180^{\circ}[/tex]
[tex]2x^{\circ}=90^{\circ}[/tex]
[tex]x^{\circ}=\frac{90}{2}=45^{\circ}[/tex]
Hence, the measure of base angle is 45°
