Question

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

Explanation:

Step1: Set up equation for (a)

Since sum of angles in a triangle is 180 degrees, for triangle (a) with angles $90^{\circ},x^{\circ},(x - 10)^{\circ}$, we have $90+x+(x - 10)=180$.
Simplify the left - hand side: $90+x+x - 10=180$, which becomes $80 + 2x=180$.
Subtract 80 from both sides: $2x=180 - 80=100$.
Divide both sides by 2: $x = 50$.

Step2: Set up equation for (b)

For an isosceles triangle (b) with angles $x^{\circ},(x + 15)^{\circ},(x + 15)^{\circ}$, we have $x+(x + 15)+(x + 15)=180$.
Simplify the left - hand side: $x+x + 15+x + 15=180$, which is $3x+30 = 180$.
Subtract 30 from both sides: $3x=180 - 30 = 150$.
Divide both sides by 3: $x = 50$.

Step3: Set up equation for (c)

For triangle (c) with angles $2x^{\circ},3x^{\circ},5x^{\circ}$, we have $2x+3x+5x=180$.
Combine like terms on the left - hand side: $10x=180$.
Divide both sides by 10: $x = 18$.

Answer:

(a) $x = 50$
(b) $x = 50$
(c) $x = 18$