Question

geometry 〉 ★ f.2 triangle angle - sum theorem ubu
questions time smartscore
13 05:47 72
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the diagram shows a triangle.
(shows a triangle with angles s - 45°, 96°, 31°)
what is the value of s?
s = °

Explanation:

Step1: Recall Triangle Angle-Sum Theorem

The sum of the interior angles of a triangle is \(180^\circ\). So, we can set up the equation: \((s - 45^\circ)+ 96^\circ+ 31^\circ= 180^\circ\).

Step2: Simplify the left - hand side of the equation

First, add the known angles: \(96^\circ+ 31^\circ = 127^\circ\). The equation becomes \((s - 45^\circ)+ 127^\circ= 180^\circ\).

Step3: Isolate the term with \(s\)

Subtract \(127^\circ\) from both sides of the equation: \(s - 45^\circ=180^\circ - 127^\circ\). Calculate \(180^\circ - 127^\circ = 53^\circ\), so \(s - 45^\circ= 53^\circ\).

Step4: Solve for \(s\)

Add \(45^\circ\) to both sides of the equation: \(s=53^\circ + 45^\circ\). Then \(s = 98^\circ\).

Answer:

\(98\)