Given
\qquad m \angle ABDm∠ABDm, angle, A, B, D is a straight angle.
\qquad m \angle ABC = 2x + 50^\circm∠ABC=2x+50
∘
m, angle, A, B, C, equals, 2, x, plus, 50, degrees
\qquad m \angle CBD = 6x + 2^\circm∠CBD=6x+2
∘
m, angle, C, B, D, equals, 6, x, plus, 2, degrees
Find m\angle CBDm∠CBDm, angle, C, B, D:
Answers
Answered by
5
Answer:
Given:
M ∠ ABD is a straight angle. ∠ ABC = 2x + 50∘ ∠ CBD = 6x + 2∘
To find:
Find m ∠ CBD
Solution:
From given, we have,
∠ ABD = 180°
∠ ABC = 2x + 50∘ ∠ CBD = 6x + 2∘
Consider the attached figure while going through the following steps.
∠ ABC + ∠ CBD = 2x + 50° + 6x + 2°
180° = 8x + 52°
180° - 52° = 8x
128° = 8x
∴ x = 16°
Now consider,
∠ ABC = 2x + 50° = 2(16) + 50 = 82°
∠ CBD = 6x + 2° = 6(16) + 2 = 98°
∴ ∠ ABC = 82° and ∠ CBD = 98°
Answered by
3
∠
A
B
D
=
=
49
∘
∠
C
B
D
=
28
∘
Explanation:
∠
A
B
C
=
∠
A
B
D
+
∠
C
B
D
77
=
(
3
x
+
22
)
+
(
5
x
−
17
)
77
=
8
x
+
5
8
x
=
77
−
5
=
72
x
=
72
8
=
9
∠
A
B
D
=
(
3
(
9
)
+
22
)
=
49
∘
∠
C
B
D
=
(
5
(
9
)
−
17
)
=
28
∘
Check:
∠
A
B
C
=
∠
A
B
D
+
∠
C
B
D
=
77
∘
=
49
∘
+
28
∘
√
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