Question

in the convex quadrilateral (abcd), if (angle acongangle d), and (mangle b = 98^{circ}), (mangle c = 50^{circ}), find (mangle a).

_________ degrees

question 8

1 pts

in the convex quadrilateral (abcd), if (angle acongangle d), and (mangle b = 112^{circ}), (mangle c = 62^{circ}), find (mangle a).

_________ degrees

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\).

Step2: Set up the equation

Let \(m\angle A = m\angle D=x\). Then \(x + x+98^{\circ}+50^{\circ}=360^{\circ}\).

Step3: Simplify the equation

\(2x+148^{\circ}=360^{\circ}\).

Step4: Solve for \(x\)

\(2x=360^{\circ}-148^{\circ}\), \(2x = 212^{\circ}\), \(x=\frac{212^{\circ}}{2}=106^{\circ}\).

For the second problem:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\).

Step2: Set up the equation

Let \(m\angle A = m\angle D=x\). Then \(x + x+112^{\circ}+62^{\circ}=360^{\circ}\).

Step3: Simplify the equation

\(2x+174^{\circ}=360^{\circ}\).

Step4: Solve for \(x\)

\(2x=360^{\circ}-174^{\circ}\), \(2x = 186^{\circ}\), \(x=\frac{186^{\circ}}{2}=93^{\circ}\).

Answer:

106
93