Two adjacent angles, ∠1
and ∠2
, form a resulting angle with measure 135° . If m∠1=(2x)° and m∠2=(2x+7)° , what are the two unknown angle measures?(1 point)
Let's assume that angle 1 is (2x)° and angle 2 is (2x+7)°.
Since the two angles are adjacent, their measures add up to the measure of the resulting angle. So, we can set up the equation:
(2x)° + (2x+7)° = 135°
Simplifying the equation:
4x + 7 = 135
4x = 128
x = 32
Therefore, angle 1 is (2x)°.
angle 1 = 2(32)° = 64°
And angle 2 is (2x+7)°.
angle 2 = 2(32)+7° = 71°
So, the two unknown angle measures are 64° and 71°.
A figure displays two complementary nonadjacent angles. If one of the angles has a measure of 39° , what is the other angle measure?(1 point)
Complementary angles are two angles that add up to 90°.
If one of the angles has a measure of 39°, then the other angle would be:
90° - 39° = 51°
So the other angle measure is 51°.
A figure shows two nonadjacent angles with measures (2x+3)° and 2x° . If the angles are complementary, what is the equation for the angle measures?(1 point)
Complementary angles are two angles that add up to 90°.
If the two angles in the figure are complementary, we can set up the equation:
(2x+3)° + 2x° = 90°
Simplifying the equation:
4x + 3 = 90
4x = 87
x = 21.75
So, the equation for the angle measures is (2x+3)° and 2x°, where x = 21.75.
Two complementary angles have measures (2x)° and (3x)° . What is the value of x and the two angle measures?(2 points)
Complementary angles are two angles that add up to 90°.
If the two angles have measures (2x)° and (3x)°, we can set up the equation:
(2x)° + (3x)° = 90°
Combining like terms:
5x = 90
Dividing both sides by 5:
x = 18
So, the value of x is 18.
Now we can substitute this value of x back into the angle measures:
Angle 1: (2x)° = 2(18)° = 36°
Angle 2: (3x)° = 3(18)° = 54°
Therefore, the value of x is 18 and the two angle measures are 36° and 54°.
Angles j and k are supplementary angles. What is m∠j if m∠k=117° ?(1 point)
If two angles are supplementary, their measures add up to 180°.
From the given information, we know that m∠k = 117°.
Since m∠j + m∠k = 180°, we can substitute the value of m∠k to find m∠j:
m∠j + 117° = 180°
Subtracting 117° from both sides:
m∠j = 63°
Therefore, m∠j is 63°.
Two supplementary angles have measures m∠ABC=105° and m∠CBD=(3x−24)° . What is the equation to solve for x ? (1 point)
(3x−24)°+
°=
°