in each of the figures given below, find the value of x:
Answers
Answer:
(i) x = 111 degrees
(ii) x = 63 degrees
Step-by-step explanation:
(i) Sum of angles of a quadrilateral ABCD is 360 degree.
=> 93 + 108 + 90 + (180 - x) = 360
=> 471 - x = 360
=> x = 111 degrees
(ii) Sum of angles of quadrilateral ABCD = 360 degree
=> 105 + 84 + x + (180 - 72) = 360
=> x + 297 = 360
=> x = 63 degrees
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Answer:
(i) x = 111°
(ii) x = 63°
Step-by-step explanation:
(i)
In Figure 1,
∠A = 93°
∠B = 90°
∠D = 108°
Now, In a Quadrilateral,
All angles add upto 360°
Thus,
∠A + ∠B + ∠C + ∠D = 360°
93° + 90° + ∠C + 108° = 360°
∠C + 291° = 360°
∠C = 360° - 291°
∠C = 69°
Now,
∠DCB + ∠DCE = 180° [Linear Pair] [BE is a straight line]
69° + x = 180°
x = 180° - 69°
x = 111°
(ii)
In Figure 2,
∠A = 105°
∠B = x
∠C = 84°
Now,
AE is a straight line.
So,
∠CDA + ∠CDE = 180° [Linear Pair]
∠D + 72° = 180°
∠D = 180° - 72°
∠D = 108°
Now,
In Quadrilateral ABCD,
∠A + ∠B + ∠C + ∠D = 360° [Angle Sum Property]
105° + x + 84° + 108° = 360°
x + 297° = 360°
x = 360° - 297°
x = 63°
Hope it helped and believing you understood it........All the best