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In the figure above, lines are drawn at the vertices of the quadrilateral as shown. What is the sum of the degree measures of the marked angles? – OGQR 2020 Question #92 with Solution

OGQR 2020: Question No. 92

In the figure above, lines are drawn at the vertices of the quadrilateral as shown. What is the sum of the degree measures of the marked angles?

SourceOGQR 2020
TypeProblem Solving
TopicGeometry
Sub-TopicQuadrilateral
DifficultyMedium

Solution

Given

In this question, we are given

  • The figure of a quadrilateral, in which lines are drawn at the vertices of the quadrilateral.

To Find

We need to determine

  • The sum of the degree measures of the marked angles.

Approach & Working

We can say

  • The sum of the marked angles = Total angles on the 4 straight lines – Sum of the interior angles of the quadrilateral.
    • Sum of interior angles of polygon of 4 sides = (4 – 2) *1800 =3600
  • Hence, sum of the marked angles = 4 * 180° – 360° = 720° – 360° = 360°

Hence, the correct answer is option B.

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