MCQ
If three angles of a quadrilateral are each equal to $75^{\circ}$, the fourth angle is.
- A$150^{\circ}$.
- ✓$135^{\circ}$.
- C$45^{\circ}$.
- D$75^{\circ}$.
✓
Answer
Correct option: B.
$135^{\circ}$.
B. $135^{\circ}$
Solution:
Given, three angles of quadrilaterals $=75^{\circ}$
Let the fourth angle be $x^{\circ}$ Then, according to the property, $75^{\circ}+75^{\circ}+75^{\circ}+x^{\circ}=360^{\circ}$, since sum of the angles of a quadrilateral is $360^{\circ}$.
So, $225^{\circ}+x^{\circ}=360^{\circ}$ or $x^{\circ}=360^{\circ}-225^{\circ}=135^{\circ}$
Hence, the fourth angle is $135^{\circ}$.
Solution:
Given, three angles of quadrilaterals $=75^{\circ}$
Let the fourth angle be $x^{\circ}$ Then, according to the property, $75^{\circ}+75^{\circ}+75^{\circ}+x^{\circ}=360^{\circ}$, since sum of the angles of a quadrilateral is $360^{\circ}$.
So, $225^{\circ}+x^{\circ}=360^{\circ}$ or $x^{\circ}=360^{\circ}-225^{\circ}=135^{\circ}$
Hence, the fourth angle is $135^{\circ}$.
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