Question

The measure of ∠x in the given figure is .

• A. ${120}^o$
• B. ${100}^o$
• C. ${90}^o$
• D. ${110}^o$

Answer 1

The correct option is D ${110}^o$


Angle sum property of a triangle is the sum of all the interior angles of a triangle is 180°.

In △XAZ,
⇒ ∠XAZ + ∠AXZ + ∠XZA = 180°
⇒ ∠XAZ + 35° + 25° = 180°
⇒ ∠XAZ + 60° = 180°
⇒ ∠XAZ = 180° - 60° = 120°


We can see that ∠XAZ is an exterior angle to △YAZ.
So, ∠XAZ and ∠YAZ are adjacent angles forming a linear pair on straight line XY.

∴ ∠YAZ + ∠XAZ = 180°
⇒ ∠YAZ + 120° = 180°
⇒ ∠YAZ = 180° - 120° = 60°

Similarly, ∠YZA and ∠YZT are adjacent angles forming a linear pair on straight line AT.

∴ ∠YZT + ∠YZA = 180°
⇒ ∠YZA + 130° = 180°
⇒ ∠YZA = 180° - 130° = 50°

In △YAZ,
⇒ ∠YAZ + ∠YZA + ∠AYZ = 180°
⇒ 60° + 50° + ∠AYZ= 180°
⇒ 110° + ∠AYZ = 180°
⇒ ∠AYZ = 180° - 110° = 70°

Again, ∠AYZ and ∠AYQ are adjacent angles forming a linear pair on straight line ZQ.

∴ ∠AYZ + ∠AYQ = 180°
⇒ ∠AYQ + 70° = 180°
⇒ ∠AYQ = 180° - 70° = 110°

So, value of x is 110°.