Question

what is the value of m?
abcd is a quadrilateral.
what is the value of a?
abcd is a quadrilateral.
what is the measure of ∠bad?

Explanation:

Step1: Recall triangle angle - sum property

The sum of interior angles of a triangle is 180°. For the first triangle with one angle 70°, if it is an isosceles triangle (judging from the marks on the sides), the other non - marked angle is also 70°. Then $m=180-(70 + 70)=40$.

Step2: Recall quadrilateral angle - sum property

The sum of interior angles of a quadrilateral is 360°. For the second quadrilateral ABCD, we have $a + 106+93 + 47=360$. So $a=360-(106 + 93+47)=114$.

Step3: Use quadrilateral angle - sum property

For the third quadrilateral ABCD, $x + 4x+3x + 2x=360$. Combining like terms, we get $10x = 360$, so $x = 36$. Then $\angle BAD=4x=4\times36 = 144$.

Answer:

For the first question, the value of $m$ is 40.
For the second question, the value of $a$ is 114.
For the third question, the measure of $\angle BAD$ is 144.