To determine the size of angle $m$, we will use the properties of angles in a quadrilateral.

Step 1: Identify the known angles

• Given angles: $86^\circ$ and $67^\circ$.
• The small square at the bottom right indicates a right angle, which is $90^\circ$.

Step 2: Use the sum of interior angles in a quadrilateral

The sum of the angles in a quadrilateral is always $360^\circ$.

$\text{Sum of all angles} = 360^\circ$

$86^\circ + 67^\circ + 90^\circ + m = 360^\circ$

Step 3: Solve for $m$

$m = 360^\circ - (86^\circ + 67^\circ + 90^\circ)$

$m = 360^\circ - 243^\circ$

$m = 117^\circ$

Thus, the value of angle $m$ is 117°.

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Related Questions:

1. What is the sum of angles in a triangle?
2. How do right angles affect calculations in geometry?
3. What are the properties of a quadrilateral?
4. How do you find missing angles in polygons?
5. Can the sum of interior angles be used in pentagons and hexagons?

Tip: Always check for right angles in geometry problems; they