Two angles of a quadrilateral are 120° and 100°. If
the remaining two angles are same, find the measure
of each angle.
Answers
Answer:
A = 120⁰
B = 100⁰
and C = D let it be 'x'
- A+ B+ C+ D = 360⁰
- 120⁰ + 100⁰ + x + x = 360⁰
- 220⁰ + 2x = 360⁰
- 2x = 360⁰ - 220⁰
- 2x = 140⁰
- x = 140⁰/2
- x = 70⁰
therefore, C = 70⁰
D = 70⁰
thanks........
★ Given:
Two angles of a quadrilateral are 120° and 100°.
The other two angles have the same measure.
★ To Find:
The measure of each angle.
★ Analysis
In this question, we will have to apply the angle sum property of quadrilaterals to derive the answer.
★ Solution:
As per the angle sum property of a quadrilateral, the sum of all the angles of a quadrilateral is 360°.
Let the equal angles be x.
Forming an equation:
120 + 100 + x + x = 360°
220 + 2x = 360°
2x = 360 - 220
2x = 140
x= 140/2
x = 70°
Hence the equal angles of the quadrilateral are 70° each.
★ Verification:
We can verify whether our answer is right by applying the newly found value into the equation.
120 + 100 + x + x = 360°
Substituting the value of x:
120 + 100 + 70 + 70 = 360°
LHS = RHS
Hence verified!
Knowledge Bytes:
→ Angle sum property of a quadrilateral
The angle sum property of a quadrilateral states that the sum of all the angles of a quadrilateral is 360°.