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Triangle NOP is formed by connecting the midpoints of the side of triangle

KLM. The measures of the interior angles of triangle KLM are shown.

Find the measure of ZMOP. Figures not necessarily drawn to scale.

K

34°

P

M

72°

N

74

L

Triangle NOP is formed by connecting the midpoints of the side of triangle KLM The measures of the interior angles of triangle KLM are shown

Answer :

ZMOP must have a measure of 60°.

What is triangle?

A triangle is a three-sided polygon that is one of the most basic shapes in geometry. It is defined by three points, known as its vertices, and the straight lines connecting them. Triangles come in many different shapes and sizes, and can be classified by their angles, sides, and area. Triangles have many uses in mathematics, for example, to calculate interior angles, calculate area and perimeter, or to prove certain geometric theorems.

In order to find the measure of ZMOP, we must first look at the structure of triangle NOP. Since it is formed by connecting the midpoints of the sides of triangle KLM, it can be classified as an equilateral triangle. This means that all three of its interior angles are equal in measure. Therefore, ZMOP must have a measure of 60°. This is because the sum of all three interior angles of an equilateral triangle is 180°, and since the other two angles have measures of 34° and 74°, the third angle must have a measure of 180° - (34° + 74°) = 60°.

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