Two complementary angles have measures (2x)° and (3x)°. What is the value of x and the two angle measures?(2 points)
x= _ (2x)°= °_ and (3x)°= _°
Since two complementary angles add up to 90°, we can set up the equation:
2x + 3x = 90
5x = 90
x = 18
Therefore, the two angle measures are:
(2x)° = (2 * 18)° = 36°
(3x)° = (3 * 18)° = 54°
So, x = 18, the first angle is 36°, and the second angle is 54°.
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)°+
°=
°
Since two supplementary angles add up to 180°, we can set up the equation:
m∠ABC + m∠CBD = 180
105 + (3x - 24) = 180
Now, solve for x:
105 + 3x - 24 = 180
3x + 81 = 180
3x = 99
x = 33
So, the equation to solve for x is:
(3x - 24) + 105 = 180
Two angles are supplementary with measures m∠ACB=4x° and m∠BCD=(6x+50)° . What is the measure of ∠ACB ?(1 point)
m∠ACB=
Since two supplementary angles add up to 180°, we can set up the equation:
m∠ACB + m∠BCD = 180
4x + (6x + 50) = 180
Now, let's solve for x:
4x + 6x + 50 = 180
10x + 50 = 180
10x = 130
x = 13
Therefore, the measure of angle ∠ACB is:
4x = 4 * 13 = 52°
So, m∠ACB = 52°.
For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?
Vertical angles are always congruent, so m∠1 = m∠3.
Given that:
m∠1 = 2x + 26
m∠3 = 3x + 32
Since m∠1 = m∠3, we can set up the equation:
2x + 26 = 3x + 32
Now, let's solve for x:
2x - 3x = 32 - 26
-x = 6
x = -6
Now that we have found the value of x as -6, we can substitute it back into either equation to find the measures of the angles:
m∠1 = 2(-6) + 26 = -12 + 26 = 14°
m∠3 = 3(-6) + 32 = -18 + 32 = 14°
Therefore, the measure of ∠1 is 14° and the measure of ∠3 is also 14°.
In a diagram, ∠A and ∠B are vertical angles, and ∠B is a complementary angle with ∠C . If m∠A=22° , write an equation that you can use to solve for m∠C .
Since ∠A and ∠B are vertical angles, they are congruent. If ∠B is a complementary angle with ∠C, it means that ∠B and ∠C add up to 90°.
Given that m∠A = 22°, ∠A and ∠B are vertical angles, so m∠B = 22°.
We can denote m∠C as x, and the equation can be written based on the complementary relationship between ∠B and ∠C:
m∠B + m∠C = 90
Substitute the known values into the equation:
22 + x = 90
Therefore, the equation you can use to solve for m∠C is:
22 + x = 90