In ABC, the sum of the measures of Angle A and angle B is 47°. What is the measure of Angle C ?
2 answers:
∠
A
=
32
∘
∠
B
=
96
∘
∠
C
=
52
∘
Explanation:
In a triangle, the three interior angles always add up to 180°:
Let
∠
A
=
x
⇒
∠
B
=
3
x
⇒
∠
C
=
x
+
20
∠
A
+
∠
B
+
∠
C
=
180
∘
⇒
x
+
3
x
+
x
+
20
=
180
⇒
5
x
+
20
=
180
⇒
5
x
=
160
x
=
32
Therefore,
∠
A
=
x
=
32
∘
∠
B
=
3
x
=
3
⋅
32
=
96
∘
∠
C
=
x
+
20
=
32
+
20
=
52
∘
Answer:
∠ C = 133°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , that is
∠ A + ∠ B + ∠ C = 180° ( substitute A + B = 47° )
47° + ∠ C = 180° ( subtract 47° from both sides )
∠ C = 133°
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