Question

Find X n the missing angles

Answer 1

First picture answer:

⇒Sum of interior angles of a triangle is equal to 180°

⇒This means that ∠D+∠E+∠F=180°

⇒∠D is (5x-2)°,∠E is (9x+3)°,∠F is (11x-21)°

⇒Plug in the values of the angles in the general equation above.

`(5x-2)+(9x+3)+(11x-21)=180\\`

⇒Group the like terms together and simplify.

`5x+9x+11x-2+3-21=180\\25x-20=180\\25x=180+20\\25x=200\\(25x)/(25) =(200)/(25) \\x=8`

⇒x=8°

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Second picture answer:

⇒If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

⇒ ∠C is the exterior angle.

⇒ ∠A and ∠B are the interior angles.

The above statement simply means

∠C=∠A+∠B

⇒ Given that ∠A is (13x-11)°

∠B is(4x+1)°

∠C is (18x-15)°

⇒Plug in the values of the angles and solve for x.

`(18x-15)=(13x-11)+(4x+1)\\`

⇒Group the like terms and solve.

`18x-13x-4x=-11+1+15\\x=5`

⇒ x=5°