two adjacent angles form a resulting angle with measure of 160°. m∠1 = 3x° and m∠2 = (2x +10°)
solve for x. what are the two unknown angles measurements?
The measure of the resulting angle is the sum of the measures of the two adjacent angles. Therefore, we can write the equation:
m∠1 + m∠2 = 160°
Substituting the given expressions for m∠1 and m∠2:
3x + (2x + 10°) = 160°
Combining like terms:
5x + 10° = 160°
Subtracting 10° from both sides:
5x = 150°
Dividing both sides by 5:
x = 30°
Now we can find the measure of the unknown angles by substituting x = 30°:
m∠1 = 3(30°) = 90°
m∠2 = 2(30°) + 10° = 70°
Therefore, the two unknown angles measure 90° and 70°.
two adjacent angles are on a straight line. one angle has the measure of (5x - 28)° and the other angle has a measure of (8x)°. What is the measure of the 2nd angle
Since the two angles are on a straight line, their sum is 180 degrees. We can set up the following equation:
(5x - 28) + 8x = 180
Combining like terms:
13x - 28 = 180
Adding 28 to both sides:
13x = 208
Dividing both sides by 13:
x = 16
Now, we can substitute x = 16 into the expression for the second angle:
8x = 8(16) = 128
Therefore, the measure of the second angle is 128 degrees.