Question

finding the sum of interior angles
drag a vertex of the triangle to change its shape.
double - click or double - tap a vertex or side to prevent
it from changing.
manipulate the triangle so ∠a measures 41° and ∠c measures 49°.
what is the approximate measure of ∠b?
m∠b
what is the sum of the interior angles of the triangle?
90
170
180
200

Explanation:

Step1: Recall triangle angle sum property

The sum of interior angles of a triangle is \(180^\circ\). So, for \(\triangle ABC\), \(m\angle A + m\angle B + m\angle C = 180^\circ\).

Step2: Substitute known angles

Given \(m\angle A = 41^\circ\) and \(m\angle C = 49^\circ\). Substitute these values into the formula: \(41^\circ + m\angle B + 49^\circ = 180^\circ\).

Step3: Solve for \(m\angle B\)

First, add \(41^\circ\) and \(49^\circ\): \(41^\circ + 49^\circ = 90^\circ\). Then, \(90^\circ + m\angle B = 180^\circ\). Subtract \(90^\circ\) from both sides: \(m\angle B = 180^\circ - 90^\circ = 90^\circ\).

Step4: Find sum of interior angles

From the triangle angle sum property, the sum of interior angles of a triangle is always \(180^\circ\).

Answer:

For \(m\angle B\): \(90^\circ\)
For the sum of interior angles: \(180^\circ\)