Math / Geometry

QuestionThe diagram shows a triangle.
What is the value of $s$ ? $s=\square^{\circ}$

Studdy Solution

STEP 1

1. We are given a triangle.
2. Two angles of the triangle are $52^\circ$ and $84^\circ$ .
3. We need to find the value of the third angle, $s$ .

STEP 2

1. Use the angle sum property of a triangle to find the unknown angle $s$ .

STEP 3

Use the angle sum property of a triangle, which states that the sum of the interior angles of a triangle is $180^\circ$ . Therefore, we can write:
$52^\circ + 84^\circ + s = 180^\circ$

STEP 4

Solve for $s$ by subtracting the sum of the known angles from $180^\circ$ :
$s = 180^\circ - (52^\circ + 84^\circ)$

STEP 5

Calculate the sum of the known angles:
$52^\circ + 84^\circ = 136^\circ$

STEP 6

Subtract the sum from $180^\circ$ to find $s$ :
$s = 180^\circ - 136^\circ$ $s = 44^\circ$
The value of $s$ is:
$s = \boxed{44^\circ}$

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