Work out the size of angle d in the quadrilateral.
Understand the Problem
The question asks to find the size of angle d in the given quadrilateral. To solve this we can find the interior angle of the 245 degree angle, then use the fact that all angles in a quadrilateral sum to 360 degrees.
Answer
$d = 186^\circ$
Answer for screen readers
$d = 186^\circ$
Steps to Solve
- Calculate the interior angle of the 245° angle
Since a full circle is 360°, we subtract the given exterior angle (245°) from 360° to find the interior angle. $$ 360^\circ - 245^\circ = 115^\circ $$
- Sum the known interior angles
Add the three known interior angles of the quadrilateral, which are 37°, 22°, and the calculated 115°. $$ 37^\circ + 22^\circ + 115^\circ = 174^\circ $$
- Calculate angle d
The sum of the interior angles of a quadrilateral is 360°. Subtract the sum of the known angles (174°) from 360° to find the value of angle d. $$ d = 360^\circ - 174^\circ = 186^\circ $$
$d = 186^\circ$
More Information
A quadrilateral is any four-sided, two-dimensional shape. The sum of the interior angles of any quadrilateral is always 360 degrees.
Tips
A common mistake would be to forget to convert the exterior angle to its interior counterpart before summing the angles. Another mistake might be summing to or subtracting from the wrong value; ensure you use 360 degrees as the total.
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