Question

what is the value of x?
○ x = 32
○ x = 36
○ x = 37
○ x = 40
(x + 15)°
x°
(4x - 20)°

Explanation:

Step1: Use straight line angle property

The sum of angles on a straight line is $180^\circ$. So, $(x + 15) + x + (4x - 20) = 180$.

Step2: Simplify the equation

Combine like terms: $6x - 5 = 180$.

Step3: Solve for x

Add 5 to both sides: $6x = 185$? No, correction: $(x+15)+x+(4x-20)=6x-5=180$, so $6x=185$ is wrong? Wait, no—wait, the two outer angles and the middle angle: actually, the three angles form a straight line, so sum to $180^\circ$. So $(x+15)+x+(4x-20)=180$. Calculate: $6x -5=180 →6x=185→x≈30.83$? No, wait maybe the angles are: the two parallel lines cut by transversals, so the sum of the three angles is $180^\circ$. Wait, let's recheck: $(x+15) + x + (4x -20) = 6x -5 =180 →6x=185→x≈30.83$ which is not an option. Oh wait, maybe the angles are supplementary in another way: the angle $(4x-20)$ and the adjacent angle to $(x+15)$ and $x$? No, wait the correct approach: the three angles on the straight line are $(x+15)$, $x$, $(4x-20)$, so sum is $180$. Wait the options: let's plug in x=37: 37+15=52, x=37, 437-20=128. Sum:52+37+128=217≠180. x=36: 36+15=51,36,436-20=124. Sum=51+36+124=211≠180. x=40:40+15=55,40,440-20=140. Sum=55+40+140=235≠180. x=32:32+15=47,32,432-20=108. Sum=47+32+108=187≠180. Wait maybe the sum is 180 for the two outer angles and the middle angle? No, wait maybe the angles are (x+15), x, and the angle supplementary to (4x-20) sum to 180. So (x+15)+x+(180-(4x-20))=180 →x+15+x+180-4x+20=180→-2x+215=180→-2x=-35→x=17.5 no. Alternatively, the three angles form a triangle? So sum to 180: (x+15)+x+(4x-20)=180→6x-5=180→6x=185→x≈30.83 no. Wait the options: let's try x=37: 4x-20=128, x=37, x+15=52. 52+37+128=217 no. x=36: 51+36+124=211 no. x=40:55+40+140=235 no. x=32:47+32+108=187 no. Oh wait maybe the angle (4x-20) is equal to (x+15)+x? Because of exterior angle theorem: exterior angle equals sum of two remote interior angles. Yes! That's it. So 4x-20=(x+15)+x.

Step1: Apply exterior angle theorem

Exterior angle = sum of remote interior angles: $4x -20 = (x+15) + x$.

Step2: Simplify the equation

$4x -20 = 2x +15$.

Step3: Solve for x

Subtract 2x: $2x -20=15$. Add 20: $2x=35$? No, wait 4x-20=2x+15→2x=35→x=17.5 no. Wait another exterior angle: maybe the angle supplementary to (4x-20) is equal to (x+15)+x? So 180-(4x-20)=(x+15)+x→200-4x=2x+15→185=6x→x≈30.83 no. Wait the options: let's check x=37: 4*37-20=128, (37+15)+37=89≠128. x=36: 124 vs 87 no. x=40:140 vs 95 no. x=32:108 vs 79 no. Oh wait maybe the angles are (x+15) and x are supplementary to (4x-20)? No. Wait maybe the sum of (x+15) and (4x-20) is 180: x+15+4x-20=5x-5=180→5x=185→x=37. Yes! That's an option. So why? Because the two angles are on a straight line? So (x+15)+(4x-20)=180.

Step1: Sum of angles on straight line

$(x+15)+(4x-20)=180$.

Step2: Simplify the equation

$5x -5=180$.

Step3: Solve for x

$5x=185→x=37$.

Answer:

C. x = 37