In a trapezium ABCD, AB∥CD. Calculate ∠C and ∠D if ∠A = 55° and ∠B = 70°
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In a trapezium ABCD, AB∥CD. Calculate ∠C and ∠D if ∠A = 55° and ∠B = 70°
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Answer:
In a trapezium where AB is parallel to CD, the opposite angles are supplementary. This means that:
∠A + ∠D = 180° (because ∠A is opposite ∠D)
∠B + ∠C = 180° (because ∠B is opposite ∠C)
You're given ∠A = 55° and ∠B = 70°. Let's calculate ∠C and ∠D:
∠A + ∠D = 180°
55° + ∠D = 180°
∠D = 180° - 55°
∠D = 125°
Now, use the second equation to find ∠C:
∠B + ∠C = 180°
70° + ∠C = 180°
∠C = 180° - 70°
∠C = 110°
So, ∠C is 110°, and ∠D is 125° in the trapezium.
Answer:
∠C is 125° and ∠D is 110° in the given trapezium ABCD.
Step by step Explanation:
Given that,
In a trapezium ABCD, AB∥CD, ∠A = 55° and ∠B = 70°
We have to Calculate ∠C and ∠D.
Now,
Trapezium is a quadrilateral with a pair of parallel sides
The adjacent interior angles sum up to 180°
Now,
So, if ∠A = 55° and ∠B = 70°
In question it is given that AB is parallel to CD.
➞∠A + ∠C = 180°
➞55° + ∠C = 180°
➞∠C = 180°-55°
➞∠C = 125°
Now,
➞∠B + ∠D = 180°
➞70° + ∠D = 180°
➞∠D = 180°-70°
➞∠D = 110°
So, ∠C is 125° and ∠D is 110° in the given trapezium ABCD.