Question

quadrilateral abcd has the following angle measures:
$m\angle a=?^{\circ },m\angle b = 97^{\circ },m\angle c = 47^{\circ },m\angle d = 90^{\circ }$
what is $m\angle a$?

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \(360^{\circ}\). So, \(m\angle A + m\angle B + m\angle C + m\angle D=360^{\circ}\).

Step2: Substitute the known values

We know \(m\angle B = 97^{\circ}\), \(m\angle C = 47^{\circ}\), \(m\angle D = 90^{\circ}\). Substituting these into the equation: \(m\angle A+97^{\circ}+47^{\circ}+90^{\circ}=360^{\circ}\).

Step3: Simplify the left - hand side

First, add \(97^{\circ}+47^{\circ}+90^{\circ}\): \(97 + 47+90=234\). So the equation becomes \(m\angle A+234^{\circ}=360^{\circ}\).

Step4: Solve for \(m\angle A\)

Subtract \(234^{\circ}\) from both sides of the equation: \(m\angle A=360^{\circ}-234^{\circ}\).

Answer:

\(126^{\circ}\)