Question

8 mark for review
note: figure not drawn to scale.
in the figure, the value of ( a ) is 46. what is the value of ( b + c + d )?
a 134
b 136
c 226
d 314

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral is \(360^{\circ}\). Let the interior angle adjacent to \(a\) be \(x\). Then \(x = 180 - a\) (linear - pair of angles). Since \(a = 46\), \(x=180 - 46=134\).

Step2: Use the angle - sum property of a quadrilateral

We know that \(x + b + c + d=360\) (sum of interior angles of a quadrilateral). Substitute \(x = 134\) into the equation: \(134 + b + c + d=360\).

Step3: Solve for \(b + c + d\)

Rearrange the equation \(b + c + d=360 - x\). Substitute \(x = 134\) into the equation, we get \(b + c + d=360-134 = 226\).

Answer:

C. 226