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In the quadrilateral shown here
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Updated on: 12 May 2026, 09:44
Updated on: 12 May 2026, 09:44
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\(\text { In the quadrilateral shown here, } a+b+c+d=\)
GRE In the quadrilateral shown here.png [ 91.79 KiB | Viewed 573 times ]
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GRE In the quadrilateral shown here.png [ 91.79 KiB | Viewed 573 times ]
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Re: In the quadrilateral shown here
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12 May 2026, 00:38
12 May 2026, 00:38
1
Shouldn't the sum be 360? Based on the fact that these are all exterior angles, it's summation should equal 360.
Re: In the quadrilateral shown here
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12 May 2026, 03:08
12 May 2026, 03:08
Expert Reply
\(a+b+c+d=360\)
Key Geometry Fact
The sum of the interior angles of any quadrilateral is always \(\mathbf{3 6 0}^{\circ}\). This holds regardless of the shape or orientation of the quadrilateral - whether it's a square, rectangle, trapezoid, or an irregular quadrilateral like the one shown.
Why This Is True
A quadrilateral can be divided into two triangles by drawing a diagonal. Each triangle has interior angles summing to \(180^{\circ}\), so:
\(2 \times 180^{\circ}=360^{\circ}\)
The curved arrows in the diagram indicate the four interior angles \(a^{\circ}, b^{\circ}, c^{\circ}\), and \(d^{\circ}\) of the quadrilateral, so:
\(a+b+c+d=360\)
Key Geometry Fact
The sum of the interior angles of any quadrilateral is always \(\mathbf{3 6 0}^{\circ}\). This holds regardless of the shape or orientation of the quadrilateral - whether it's a square, rectangle, trapezoid, or an irregular quadrilateral like the one shown.
Why This Is True
A quadrilateral can be divided into two triangles by drawing a diagonal. Each triangle has interior angles summing to \(180^{\circ}\), so:
\(2 \times 180^{\circ}=360^{\circ}\)
The curved arrows in the diagram indicate the four interior angles \(a^{\circ}, b^{\circ}, c^{\circ}\), and \(d^{\circ}\) of the quadrilateral, so:
\(a+b+c+d=360\)
