Question

find angle \\(b\\) in this isosceles triangle if \\(a = 46^{\circ}\\)

Explanation:

🆕 New Concept Discovered: Properties of Isosceles Triangles
Equal sides mean equal base angles

Step 1: Identify the given angles

An isosceles triangle has two equal sides and two equal base angles. From the diagram, the two base angles are both labeled \( A \), and the vertex angle is labeled \( B \).

We are given:

$$ A = 46^{\circ} $$

Since both base angles are equal to \( A \), we have two angles of \( 46^{\circ} \).

Step 2: Use the triangle angle sum theorem

The sum of all interior angles in any triangle is always \( 180^{\circ} \).

$$ A + A + B = 180^{\circ} $$

Substitute the known value of \( A \):

$$ 46^{\circ} + 46^{\circ} + B = 180^{\circ} $$

Step 3: Solve for B

Combine the base angles:

$$ 92^{\circ} + B = 180^{\circ} $$

Subtract \( 92^{\circ} \) from both sides to find \( B \):

$$ B = 180^{\circ} - 92^{\circ} $$

$$ B = 88^{\circ} $$

Answer:

88