Question

triangle abc is shown. explain why ( a + b = d )

Explanation:

Step1: Use the triangle angle - sum property

In \(\triangle ABC\), by the triangle angle - sum property, \(a + b + c=180\) (since the sum of angles in a triangle is \(180^{\circ}\)). So, \(c = 180-(a + b)\).

Step2: Use the linear - pair property

Since \(c\) and \(d\) form a linear pair (they are adjacent angles on a straight line), \(c + d=180\) (linear - pair angles are supplementary). Then \(d=180 - c\).

Step3: Substitute the value of \(c\) from Step1 into the equation from Step2

Substitute \(c = 180-(a + b)\) into \(d = 180 - c\). We get \(d=180-(180-(a + b))\).
Simplify the right - hand side: \(d = 180-180+(a + b)\).

Answer:

So, \(a + b=d\)