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?
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Geometry |
| Sub-Topic | Quadrilateral |
| Difficulty | Medium |
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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