Question

In the adjoining figure, Lines AB || CD find the value of x and y.​

Answer 1

Given

• AB || CD
• ∠APQ = 2x+10°
• ∠QPR = x-5°
• ∠DQP = 2y-10°
• ∠CRP = x+y+15°

To Find

• Value of x and y

Solution

_____________________

We know that

• If a transversal intersects two parallel lines then each pair of alternate interior angles are equal.

Therefore, ∠APQ = ∠DQP

And ∠APQ+∠QPR = ∠CRP

${~~~~\implies \sf 2x +10 = 2y -10 }$

${~~~~\implies \sf 2x - 2y+10 + 10= 0 }$

${~~~~\implies \sf 2x - 2y+20= 0 \: \: \: \: \: - - - - (1) }$

Or

${~~~~~~~~~\implies \sf (2x + 10) + (x - 5) = x + y + 15 }$

${~~~~~~~~~\implies \sf 2x + 10+ x - 5 - x - y - 15= 0 }$

${~~~~~~~~~\implies \sf 2x - y - 10= 0 \: \: \: \: \: - - - - (2) }$

• Subtracting equation 2 from 1.

${~~~~\implies \sf 2x - 2y+20 - ( 2x - y - 10) = 0}$

${~~~~\implies \sf \cancel{2x} - 2y+20 - \cancel{2x} + y + 10 = 0}$

${~~~~\implies \sf - y+30= 0}$

${~~~~\implies \sf - y= - 30}$

${~~~~\implies \sf y= 30 }$

• Putting x in Equation 1

${~~~~\implies \sf 2x - 2y+20= 0 }$

${~~~~\implies \sf 2x - 2 \times 30+20= 0 }$

${~~~~\implies \sf 2x - 60+20= 0 }$

${~~~~\implies \sf 2x - 40= 0 }$

${~~~~\implies \sf 2x = 40 }$

${~~~~\implies \sf x = 20 }$

$\mathcal{Hence \: the \: value \: of \:\red{x} \: and \: \pink{ y } \: is \: \red{20} \: and \: \pink{ 30 }\: respectively}$