To find the value of x, we can set up the equation:
2x + 3x = 90 degrees (as complementary angles add up to 90 degrees)
5x = 90
x = 90 / 5
x = 18
So, x = 18
Substitute x back into the angle measures:
(2x)° = 2 * 18 = 36°
(3x)° = 3 * 18 = 54°
Therefore, the two angle measures are:
(2x)° = 36°
(3x)° = 54°
Two complementary angles have measures (2x)° and (3x)° . What is the value of x and the two angle measures?(2 points)t
x=
, (2x)°=
°, and (3x)°=
°
11 answers
Angles j and k are supplementary angles. What is m∠j if m∠k=117° ?(1 point)
°
°
Supplementary angles add up to 180 degrees.
Given that the measure of angle k (m∠k) is 117 degrees, we can find the measure of angle j (m∠j) using the supplementary angles property:
m∠j + m∠k = 180
Substitute m∠k = 117 into the equation:
m∠j + 117 = 180
Subtract 117 from both sides:
m∠j = 180 - 117 = 63
Therefore, the measure of angle j (m∠j) is 63 degrees.
Given that the measure of angle k (m∠k) is 117 degrees, we can find the measure of angle j (m∠j) using the supplementary angles property:
m∠j + m∠k = 180
Substitute m∠k = 117 into the equation:
m∠j + 117 = 180
Subtract 117 from both sides:
m∠j = 180 - 117 = 63
Therefore, the measure of angle j (m∠j) is 63 degrees.
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)°+
°=
°
(3x−24)°+
°=
°
Since angles ABC and CBD are supplementary, their sum will be equal to 180 degrees.
The equation to solve for x is:
105° + (3x - 24)° = 180°
Therefore, the equation is:
(3x - 24)° + 105° = 180°
The equation to solve for x is:
105° + (3x - 24)° = 180°
Therefore, the equation 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=
°
m∠ACB=
°
Since the two angles are supplementary, their sum will be equal to 180 degrees.
The equation to solve for the measure of angle ACB is:
4x + 6x + 50 = 180
Combine like terms:
10x + 50 = 180
Subtract 50 from both sides:
10x = 130
Divide by 10:
x = 13
Now, substitute x back into the measure of angle ACB formula:
4x = 4 * 13 = 52
Therefore, the measure of angle ACB is 52 degrees.
The equation to solve for the measure of angle ACB is:
4x + 6x + 50 = 180
Combine like terms:
10x + 50 = 180
Subtract 50 from both sides:
10x = 130
Divide by 10:
x = 13
Now, substitute x back into the measure of angle ACB formula:
4x = 4 * 13 = 52
Therefore, the measure of angle ACB is 52 degrees.
Question
Use the image to answer the question.
An illustration shows a horizontal line intersecting two parallel slanting lines. The angles the horizontal line forms with left parallel line are 1, 2, 3, and 4. Angles 1 and 2 are complementary. Angles 2 and 4 are complementary. Angles 4 and 3 are complementary. Angles 3 and 1 are complementary. Angles 1 and 4 are opposite each other. Angles 2 and 3 are opposite each other. The angles the horizontal line forms with right parallel line are 5, 6, 7, and 8. . Angles 5 and 6 are complementary. Angles 6 and 8 are complementary. Angles 8 and 7 are complementary. Angles 7 and 5 are complementary. Angles 5 and 8 are opposite each other. Angles 6 and 7 are opposite each other.
Which angle is a vertical angle with ∠5 ?
(1 point)
∠
Use the image to answer the question.
An illustration shows a horizontal line intersecting two parallel slanting lines. The angles the horizontal line forms with left parallel line are 1, 2, 3, and 4. Angles 1 and 2 are complementary. Angles 2 and 4 are complementary. Angles 4 and 3 are complementary. Angles 3 and 1 are complementary. Angles 1 and 4 are opposite each other. Angles 2 and 3 are opposite each other. The angles the horizontal line forms with right parallel line are 5, 6, 7, and 8. . Angles 5 and 6 are complementary. Angles 6 and 8 are complementary. Angles 8 and 7 are complementary. Angles 7 and 5 are complementary. Angles 5 and 8 are opposite each other. Angles 6 and 7 are opposite each other.
Which angle is a vertical angle with ∠5 ?
(1 point)
∠
Vertical angles are formed by two intersecting lines, and they are always congruent (have the same measure).
In the given case, the angles 5 and 8 are opposite each other. Since opposite angles are vertical angles, ∠8 is a vertical angle with ∠5.
In the given case, the angles 5 and 8 are opposite each other. Since opposite angles are vertical angles, ∠8 is a vertical angle with ∠5.
Use the image to answer the question.
An illustration shows five rays emerging from a point labeled A, forming the following angles from left to right: 1, 2, 3, 4, and 5. Angles 1 and 2 together form a right angle.
If m∠2=47° , what is m∠4 ?
(1 point)
°
An illustration shows five rays emerging from a point labeled A, forming the following angles from left to right: 1, 2, 3, 4, and 5. Angles 1 and 2 together form a right angle.
If m∠2=47° , what is m∠4 ?
(1 point)
°
Since angles 1 and 2 form a right angle, we know that the sum of their measures is 90 degrees.
m∠1 + m∠2 = 90°
m∠1 + 47° = 90°
m∠1 = 90° - 47°
m∠1 = 43°
Since angles 1 and 4 are supplementary angles (they form a straight line), their sum is 180 degrees.
m∠1 + m∠4 = 180°
43° + m∠4 = 180°
m∠4 = 180° - 43°
m∠4 = 137°
Therefore, the measure of angle 4 (m∠4) is 137 degrees.
m∠1 + m∠2 = 90°
m∠1 + 47° = 90°
m∠1 = 90° - 47°
m∠1 = 43°
Since angles 1 and 4 are supplementary angles (they form a straight line), their sum is 180 degrees.
m∠1 + m∠4 = 180°
43° + m∠4 = 180°
m∠4 = 180° - 43°
m∠4 = 137°
Therefore, the measure of angle 4 (m∠4) is 137 degrees.