Question

find the value of in the triangle shown below.
x=
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angles in a triangle sum to 180° proof

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, if the angles of the triangle are \(85^{\circ}\), \(67^{\circ}\), and \(x^{\circ}\), then \(85 + 67+x=180\).

Step2: Simplify the left - hand side of the equation

First, add \(85\) and \(67\): \(85 + 67=152\). The equation becomes \(152+x = 180\).

Step3: Solve for \(x\)

Subtract \(152\) from both sides of the equation. \(x=180 - 152\).
\(x = 28\)

Answer:

\(28\)