Question

Toping asked Oct 3, 2023

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1 Answer

Feroze · Answer 1 · 2023-10-07T06:25:29+0000

Answer:

3. x = 4

4. x = 9

Explanation:

Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

Apply the Exterior Angle Theorem.

$\implies (11x-2)^(\circ)+(9x+1)^(\circ)=(19x+3)^(\circ)$

$\implies 11x-2+9x+1=19x+3$

$\implies 20x-1=19x+3$

$\implies 20x-1+1=19x+3+1$

$\implies 20x=19x+4$

$\implies 20x-19x=19x+4-19x$

$\implies x=4$

Apply the Exterior Angle Theorem.

$\implies (7x+2)^(\circ)+(7x+2)^(\circ)=(17x-23)^(\circ)$

$\implies 7x+2+7x+2=17x-23$

$\implies 14x+4=17x-23$

$\implies 14x+4-4=17x-23-4$

$\implies 14x=17x-27$

$\implies 14x-17x=17x-27-17x$

$\implies -3x=-27$

$\implies x=9$

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