Question

the diagram shows a triangle. what is the value of x? x =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°.

Step2: Set up an equation

Let the three interior angles of the triangle be 35°, 62°, and the third - angle which is supplementary to \(x + 29^{\circ}\). The third - angle is \(180-(x + 29)=151 - x\). Then \(35+62+(151 - x)=180\).

Step3: Simplify the left - hand side of the equation

\(35+62+151 - x=248 - x\). So, \(248 - x = 180\).

Step4: Solve for x

Add x to both sides: \(248=180 + x\). Then subtract 180 from both sides: \(x=248 - 180=68\).

Answer:

68