Question

Two adjacent angles on a straight line are in ratio of 5:4.Find the measure of each angle.In the figure 2,AB is parallel to CD.Prove that p+q-r=180.

Answer 1

$\huge\bigstar\underline\mathcal\blue{Answer:-}$

1. Let first angle = 5x

and second angle = 4x

we know, sum of two adjacent angles =180°

so,

5x + 4x = 180°

9x = 180°

x = 20°

so, first angle = 5x = 5×20=100°

second angle = 4x =4×20= 80°

2. Draw a line 'l' parallel to AB and CD through F.

From the figure

p° + x° =180° ____(1)

Sum of interior angles same side of the transversal are supplementary

r° = y°---(2)______alternate angles

Therefore,

x° + y° = q°

=> x° = q° - y°

=> x° = q° - r° --(3) _____ From (2)

Now, put (3) in equation (1), we get

p° + q° - r° = 180°

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