Find the measure of x in the given figure.
Answers
⇒ Final answer:
x = 65°
⇒ Given:
A quadrilateral with 3 exterior angles and 1 interior angle marked.
⇒ To Find:
The exterior angle x.
⇒ Formula to be used:
→ Sum of all exterior angles = 360°
⇒ Solution:
We have got the measures of 2 exterior angles as 110° and 90°.
How did we get this?
In the upper left angle of the quadrilateral, it is marked 110° and the right angle of the quadrilateral is marked with a square. A square angle always denotes 90°.
Next, we have the interior angle marked as 85°.
In order to find the exterior angle marked on that side, we need to use the formula:
180° - Interior angle = Exterior angle
How did we get this?
An interior angle and an exterior angle together form a straight line. This means that the sum of both the angles is 180°. So, if we have got the value of either interior or exterior angle, we can get the value of the other angle.
Therefore,
180° - 85° = Exterior angle
180 - 85 = 95°
Hence the exterior angle is 95°.
Thus, we have got the value of three exterior angles: 110°, 90° and 95°.
Now, we have to find the value of angle x.
How to do it?
In this part, the only formula and concept that we can use is the sum of exterior angle property of a quadrilateral. This means that the sum of the exterior angles of any quadrilateral will always be 360°.
So,
360° - Sum of given exterior angles = Unknown value
Given exterior angles:
110°, 90° and 95°.
Sum of these exterior angles:
110 + 90 + 95 = 295°
Now, putting these values in the formula:
360 - 295 = unknown angle x
x = 360 - 295
x = 65°
Hence the value of the unknown angle, x is 65°.
Exterior angle property of a quadrilateral:
From the exterior angle property of a quadrilateral, we know that the sum of all the 4 exterior angles of a quadrilateral is always equal to 360°.