Question

name angles of a triangle the sum of the angles in a triangle = 180 degrees calculate x in each of these diagrams.

Explanation:

Step1: Set up equation for (a)

Since the sum of angles in a triangle is 180 degrees, for triangle (a) we have $x+(x - 10)+90=180$.

Step2: Simplify the equation for (a)

Combine like - terms: $2x-10 + 90=180$, which simplifies to $2x+80 = 180$.

Step3: Solve for x in (a)

Subtract 80 from both sides: $2x=180 - 80=100$. Then divide by 2, so $x = 50$.

Step4: Set up equation for (b)

For triangle (b), since it is an isosceles triangle (equal sides), the two base angles are equal. So $x+(x + 15)+(x + 15)=180$.

Step5: Simplify the equation for (b)

Combine like - terms: $3x+30 = 180$.

Step6: Solve for x in (b)

Subtract 30 from both sides: $3x=180 - 30 = 150$. Then divide by 3, so $x = 50$.

Step7: Set up equation for (c)

For triangle (c), $2x+5x+3x=180$.

Step8: Simplify the equation for (c)

Combine like - terms: $10x=180$.

Step9: Solve for x in (c)

Divide both sides by 10, so $x = 18$.

Step10: Set up equation for (d)

For triangle (d), $(x + 14)+(2x - 10)+x=180$.

Step11: Simplify the equation for (d)

Combine like - terms: $4x+4 = 180$.

Step12: Solve for x in (d)

Subtract 4 from both sides: $4x=180 - 4 = 176$. Then divide by 4, so $x = 44$.

Step13: Set up equation for (e)

For triangle (e), $(x + 20)+10x+(x + 16)=180$.

Step14: Simplify the equation for (e)

Combine like - terms: $12x+36 = 180$.

Step15: Solve for x in (e)

Subtract 36 from both sides: $12x=180 - 36 = 144$. Then divide by 12, so $x = 12$.

Answer:

(a) $x = 50$
(b) $x = 50$
(c) $x = 18$
(d) $x = 44$
(e) $x = 12$