ABCD is a trapezium in which ab parallel DC if angleA is equal to 50 degree and Angle B 70 degree find the measure of the other two angle
Answers
Answer:
∠ D = 130° ∠ C = 110°
Step-by-step explanation:
In trapezium ABCD,
AB ║ CD
and ∠ A = 50° , ∠ B = 70°
Now AD as a transversal to parallel lines AB and CD,
∠ A + ∠ D = 180° ( ∵ interior angles on the same side of transversal)
⇒ 50° + ∠ D = 180°
⇒ ∠ D = 130°
Now BC as a transversal to parallel lines AB and CD,
∠ B + ∠ C = 180° ( ∵ interior angles on the same side of transversal)
⇒ 70° + ∠ C = 180°
⇒ ∠ C = 110°
Step-by-step explanation:
search-icon-header
Search for questions & chapters
search-icon-image
Class 9
>>Maths
>>Quadrilaterals
>>Quadrilaterals and Their Various Types
>>In quadrilateral ABCD , side AB is paral
Question
Bookmark
In quadrilateral ABCD, side AB is parallel to side DC. If ∠A:∠D=1:2 and ∠C:∠B=4:5
Calculate each angle of the quadrilateral.
Medium
Solution
verified
Verified by Toppr
Given
∠A:∠D=1:2
Let us consider ∠A=x and ∠D=2x
∠C:∠B=4:5
Let us consider ∠C=4y and ∠B=5y
Also, given
AB∣∣DC and the sum of opposite angles of quadrilateral is 180
o
So.
∠A+∠D=180
o
x+2x=180
o
3x=180
o
We get,
x=60
o
Therefore, ∠A=60
o
∠D=2x
2×60
o
=120
o
Therefore, ∠D=120
o
Now,
∠B+∠C=180
o
5y+4y=180
o
9y=180
o
We get,
y=20
o
∠B=5y=5×20
o
=100
o
∠C=4y=4×20
o
=80
o
Therefore, ∠A=60
o
,∠B=100
o
,∠C=80
o
and ∠D=120
o