Question

what is the sum of all the angle measures in the diagram?
(m∠1 + m∠4) + (m∠2 + m∠5) + (m∠3 + m∠6) =◻
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Explanation:

Step1: Recognize triangle angle sum

Each group of three angles (∠1 + ∠4, ∠2 + ∠5, ∠3 + ∠6) forms a triangle's interior angles. A triangle's angle sum is \(180^\circ\).

Step2: Calculate total sum

There are 3 such triangles (or 3 groups). So total sum is \(3\times180^\circ = 540^\circ\).

Answer:

540