Question

In fig. 9. 20, DE ll BC find the value of X,y,z​

Answer 1

$\huge\mathtt{{\fcolorbox{gold}{gold}{AnSwEr~~~↓}}}$

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$\bold{Given:}$

DE || BC.

$\bold{To~find:}$

The angles x, y and z

Here, ∠CAE=∠BCA (Alternate Interior Angles)

$\therefore$ ∠z = 55°

$\bold{Here:}$

∠CBA + ∠BAC + ∠BCA = 180° (Angle Sum Property of a Triangle)

$\implies$ 45° + x + 55° = 180°

$\implies$ 100° + x = 180°

$\implies$ x = 180° - 100°

$\implies$ x = 80°

$\bold{Also:}$

∠DAB + ∠BAC + ∠CAE = 180° (Straight Line)

$\implies$ y + 80° + 55° = 180°

$\implies$ y + 135° = 180°

$\implies$ y = 180° - 135°

$\implies$ y = 45°

$\bold{Required~answer:}$

• x = 80°
• y = 45°
• z = 55°

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$\huge\mathrm\color{gold}{Hope~it~helps..!!}$