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An irregular pentagon is shown below.

Calculate the size of the angle marked m.
m
25°
com
86
72°

An irregular pentagon is shown below. Calculate the size of the angle marked m. m-example-1

1 Answer

1 vote

The angle marked with an "m" in the image is 77 degrees.

To calculate this, we can use the following steps:

Step 1: Draw a diagonal from vertex A to vertex E, dividing the pentagon into two triangles.

Step 2: Calculate the sum of the interior angles in triangle ADE. Since the sum of the interior angles in any triangle is 180 degrees, we have:

Angle ADE + Angle AED + Angle EAD = 180 degrees

From the image, we see that Angle ADE = 25 degrees and Angle AED = 86 degrees. Therefore, Angle EAD = 180 degrees - 25 degrees - 86 degrees = 69 degrees.

Step 3: Calculate the sum of the interior angles in triangle ABE. Since the sum of the interior angles in any triangle is 180 degrees, we have:

Angle ABE + Angle ABM + Angle EBM = 180 degrees

From the image, we see that Angle ABE = 72 degrees and Angle ABM = 01 degrees. Therefore, Angle EBM = 180 degrees - 72 degrees - 01 degrees = 107 degrees.

Step 4: Since Angle EAD and Angle EBM are supplementary angles, their sum is equal to 180 degrees. Therefore, Angle m = 180 degrees - Angle EBM = 180 degrees - 107 degrees = 73 degrees.

Therefore, the angle marked with an "m" in the image is 77 degrees.

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