1.

Find the value of ‘x’ in the given figure.

Answer»

In the given figure, 

∠HAC = ∠TAE = a (∵ Vertically opposite angles) 

In ∆AHC, 

we know, ∠H + ∠C + ∠HAC 180° 

⇒ 60° + 80° + a = 180°

⇒ 140° + a – 140° = 180°- 140° … a = 40°. 

∴ ∠HAC = ∠TAE = a = 40° 

In ∆ATE, we know, 

∠T + ∠TAE + ∠E = 180° 

⇒ x + a + 70° = 180° 

⇒ x + 40° + 70° = 180° 

⇒ x + 110°- 110° = 180°- 110° 

∴ x = 70°



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