Two angles are supplementary. ∠QRS=x+16° and ∠SRT=3x°. What is the measure of ∠SRT?
It said they are supplementary, so their sum is 180°
3x + x+16 = 180
4x = 164
x = 41
so ∠SRT=3x = 3(41°) = 123°
To find the measure of ∠SRT, we need to use the property that supplementary angles add up to 180°.
Given that ∠QRS=x+16° and ∠SRT=3x°, we know that ∠QRS and ∠SRT are supplementary, which means their sum is equal to 180°.
Therefore, we can set up the equation:
(x + 16°) + (3x°) = 180°
Combining like terms, we get:
4x + 16° = 180°
Subtracting 16° from both sides of the equation:
4x = 180° - 16°
Simplifying:
4x = 164°
Dividing both sides of the equation by 4:
x = 164° / 4
x = 41°
Now that we know the value of x, we can substitute it back into the equation for ∠SRT:
∠SRT = 3x°
∠SRT = 3(41°)
∠SRT = 123°
Therefore, the measure of ∠SRT is 123°.
To find the measure of ∠SRT, we need to know the value of x. However, we are given that the two angles, ∠QRS and ∠SRT, are supplementary. By definition, supplementary angles add up to 180 degrees.
So, we can set up an equation to solve for x:
∠QRS + ∠SRT = 180°
Substituting the given values:
(x + 16°) + (3x°) = 180°
Combining like terms:
4x + 16° = 180°
Next, we need to isolate the variable x. Let's subtract 16 degrees from both sides of the equation:
4x + 16° - 16° = 180° - 16°
Simplifying:
4x = 164°
Finally, we can solve for x by dividing both sides of the equation by 4:
4x/4 = 164°/4
Simplifying further:
x = 41°
Now that we know the value of x, we can find the measure of ∠SRT by substituting x back into the expression for ∠SRT:
∠SRT = 3x = 3 * 41° = 123°
Therefore, the measure of ∠SRT is 123 degrees.