Question

in the convex quadrilateral abcd, if ∠a ≅ ∠d, and m∠b = 120°, m∠c = 78°, find m∠a. degrees question 15 1 pts calculate the sum of the interior angles of a convex 16 - gon. sum = degrees

Explanation:

Step1: Recall the formula for the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\). Let \(m\angle A = m\angle D=x\). Then \(x + 120^{\circ}+78^{\circ}+x=360^{\circ}\).

Step2: Simplify the equation

Combine like - terms: \(2x+198^{\circ}=360^{\circ}\).

Step3: Solve for \(x\)

Subtract \(198^{\circ}\) from both sides: \(2x=360^{\circ}- 198^{\circ}=162^{\circ}\). Then divide by \(2\): \(x = 81^{\circ}\).

Step4: Recall the formula for the sum of interior angles of an \(n\) - gon

The sum of interior angles of an \(n\) - gon is \((n - 2)\times180^{\circ}\). For \(n = 16\), the sum is \((16 - 2)\times180^{\circ}\).

Step5: Calculate the sum

\((16 - 2)\times180^{\circ}=14\times180^{\circ}=2520^{\circ}\).

Answer:

\(81\) degrees, \(2520\) degrees