In a triangle ABC, AB = BC. If ∠A = 5x and ∠C = 2x + 30°. Find ∠A and ∠C.
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1
Answer:
Step-by-step explanation:
Given:
∠
A
=
5
x
+
30
∘
,
∠
B
=
2
x
,
and
A
B
=
B
C
I am going to use the notation where the side opposite the angle has the same letter but in lowercase. In this notation, AB becomes side c and BC becomes side a, therefore, AB = BC becomes c = a
Because c = a, we know that
∠
A
=
∠
C
=
5
x
+
30
∘
; this allows us to write the following equation:
∠
A
+
∠
B
+
∠
C
=
180
∘
Substitute the corresponding functions of x:
5
x
+
30
+
2
x
+
5
x
+
30
=
180
∘
Solve for x:
12
x
+
60
2
=
180
∘
12
x
=
120
∘
x
=
10
∘
∠
C
=
5
(
10
∘
)
+
30
∘
∠
C
=
80
∘
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