Lines m and n are parallel, as shown in the diagram below. What are the measures of angles A and B?
2 answers:
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Answer:
Hence prove.
Step-by-step explanation:
Given:
∠A + ∠D = 90°
We are prove to that
Solution:
See required figure in attached file.
We know sum of the all angles of a triangle is 180°.
So, in triangle AED.
∠A + ∠E + ∠D = 180°
∠E + (∠A + ∠D) = 180°
Now, we substitute ∠A + ∠D = 90° in above equation.
∠E + 90° = 180°
∠E = 180° - 90°
∠E = 90°
Using Pythagoras Theorem for triangle ADE and triangle BEC.
Now, we add both above equations.
--------(1)
Similarly, Using Pythagoras Theorem for triangle AEC and triangle BED.
Now, we add both above equations.
--------(2)
We get From equation 1 and equation 2.
Hence prove,
