Question

For the figure shown find the value of the variable in the measures of the angles.

(it's a 4 part question)

so solve for x, then P, then Q, and finally R​

Answer 1

We know that, the sum of all the angles of a triangle is 180°.

According to the above problem,

`(2x - 20) + (2x + 15) + x = 180 \\ 2x - 20 + 2x + 15 + x = 180 \\ 5x - 5 = 180 \\ 5x = 180 + 5 \\ 5x = 185 \\ x = (185)/(5) \\ \boxed{x = 37}`

Therefore, the value of x is 37.

→ P = (2x - 20)° = {2 (37) - 20}° = 54°

→ Q = (2x + 15)° = {2 (37) + 15}° = 89°

→ R = (x)° = 37°

Answer 2

`\\ \rm\longmapsto 2x+15+2x-20+x=180`

`\\ \rm\longmapsto 5x-5=180`

`\\ \rm\longmapsto 5x=180+5=185`

`\\ \rm\longmapsto x=(185)/(5)=37`

Now

• <P=2x-20=2(37)-20=74-20=54
• <Q=2x+15=2(37+15=74+15=89