Math / Geometry

QuestionB 56°

Studdy Solution

STEP 1

1. The triangle is isosceles, meaning it has two equal sides and two equal angles.
2. One angle is given as $56^\circ$ .
3. We need to find the measure of angle $B$ , which is one of the base angles.
4. The sum of the angles in any triangle is $180^\circ$ .

STEP 2

1. Identify the known angles and sides in the triangle.
2. Use the properties of isosceles triangles to find the measure of angle $B$ .

STEP 3

In an isosceles triangle, the angles opposite the equal sides are equal. Since the angle $56^\circ$ is not one of the base angles, it must be the vertex angle. Therefore, the two base angles, which are equal, are the angles opposite the equal sides.

STEP 4

Let the measure of each base angle be $B$ . Since the sum of the angles in a triangle is $180^\circ$ , we can write:
$56^\circ + B + B = 180^\circ$

STEP 5

Simplify the equation to solve for $B$ :
$56^\circ + 2B = 180^\circ$
Subtract $56^\circ$ from both sides:
$2B = 180^\circ - 56^\circ$ $2B = 124^\circ$

STEP 6

Divide both sides by 2 to find $B$ :
$B = \frac{124^\circ}{2}$ $B = 62^\circ$
The measure of angle $B$ is:
$\boxed{62^\circ}$

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