Q: In an isosceles triangle $ABC$ with $AB = AC$, if $\angle B = 50^\circ$, then what is the measure of $\angle A$?

In $\triangle ABC$, since $AB = AC$, the angles opposite to these equal sides are also equal: $$\angle C = \angle B = 50^\circ$$ \nAccording to the Angle Sum Property of a triangle: $$\angle A + \angle B + \angle C = 180^\circ$$ $$\angle A + 50^\circ + 50^\circ = 180^\circ$$ $$\angle A + 100^\circ =

Q: In an isosceles triangle $ABC$ with $AB = AC$, if $\angle A = 80^\circ$, then what is the measure of $\angle B$?

In $\triangle ABC$, $AB = AC$, which means angles opposite to equal sides are equal.\nHence, $\angle B = \angle C$. \nSum of angles in a triangle = $180^\circ$ $$\angle A + \angle B + \angle C = 180^\circ$$ $$80^\circ + \angle B + \angle B = 180^\circ$$ $$2\angle B = 180^\circ - 80^\circ = 100^\circ

Question 1

In $	riangle ABC$ and $	riangle PQR$, $AB = PQ$, $BC = QR$, and $\angle B = \angle Q = 90^\circ$. Which congruence criterion proves that $	riangle ABC \cong 	riangle PQR$?

Accepted Answer

Given $AB = PQ$ and $BC = QR$, the included angle between sides $AB$ and $BC$ is $\angle B$, and between sides $PQ$ and $QR$ is $\angle Q$. Since $\angle B = \angle Q = 90^\circ$, two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle. Ther

Question 2

In an isosceles triangle $ABC$ with $AB = AC$, if $\angle B = 50^\circ$, then what is the measure of $\angle A$?

Accepted Answer

In $	riangle ABC$, since $AB = AC$, the angles opposite to these equal sides are also equal: $$\angle C = \angle B = 50^\circ$$ 
According to the Angle Sum Property of a triangle: $$\angle A + \angle B + \angle C = 180^\circ$$ $$\angle A + 50^\circ + 50^\circ = 180^\circ$$ $$\angle A + 100^\circ =

Question 3

In an isosceles triangle $ABC$ with $AB = AC$, if $\angle A = 80^\circ$, then what is the measure of $\angle B$?

Accepted Answer

In $	riangle ABC$, $AB = AC$, which means angles opposite to equal sides are equal.
Hence, $\angle B = \angle C$. 
Sum of angles in a triangle = $180^\circ$ $$\angle A + \angle B + \angle C = 180^\circ$$ $$80^\circ + \angle B + \angle B = 180^\circ$$ $$2\angle B = 180^\circ - 80^\circ = 100^\circ

Question 4

In $	riangle ABC$, if $AB = 5	ext{ cm}$, $BC = 7	ext{ cm}$, and $AC = 6	ext{ cm}$, which is the largest angle of the triangle?

Accepted Answer

In any triangle, the angle opposite to the longest side is always the largest angle. 
Here, the longest side is $BC = 7	ext{ cm}$.
The angle opposite to side $BC$ is $\angle A$.
Therefore, $\angle A$ is the largest angle.

Question 5

What is the measure of each interior angle of an equilateral triangle?

Accepted Answer

An equilateral triangle has all three sides equal, which means all three interior angles are also equal.
Let each angle be $x$. $$x + x + x = 180^\circ$$ $$3x = 180^\circ$$ $$x = 60^\circ$$ 
Thus, each angle of an equilateral triangle is $60^\circ$.

Triangles