In a geometric diagram, ∠A and ∠B are complementary, and they form a straight line with ∠C . If m∠A=x° , m∠B=(2x)° , and m∠C=90° , what is the measure of ∠B ?(1 point)
Since ∠A and ∠B are complementary angles and form a straight line with ∠C, we have the equation:
∠A + ∠B + ∠C = 180°
Substituting the given values, we have:
x + 2x + 90 = 180
Combining like terms:
3x + 90 = 180
Subtracting 90 from both sides:
3x = 90
Dividing both sides by 3:
x = 30
Therefore, the measure of ∠B is 2x = 2(30) = 60 degrees.
Two angles, ∠1
and ∠2
, in a diagram are complementary. If m∠2=26° , what equation can you write to solve for m∠1 ?(1 point)
Since ∠1 and ∠2 are complementary, we know that the sum of their measures is equal to 90 degrees.
We can write the equation:
m∠1 + m∠2 = 90
Substituting the given value, we have:
m∠1 + 26 = 90
This equation can be used to solve for m∠1.
In a diagram, ∠3 and ∠5 are vertical angles, and ∠4 is a supplementary angle with ∠5 . If m∠3=67° , what equation can you write to solve for m∠4 ?(1 point)
Since ∠3 and ∠5 are vertical angles, they have the same measure. Therefore, m∠3 = m∠5.
∠4 and ∠5 are supplementary angles, which means their measures add up to 180 degrees.
We can write the equation:
m∠3 + m∠4 = 180
Substituting the given value, we have:
67 + m∠4 = 180
This equation can be used to solve for m∠4.
An illustration shows a rectangle which is segmented left to right into a right triangle, a trapezoid in the middle, and another right triangle. The sides of the rectangle form the sides of the triangles. The top corners of the rectangle are denoted by two right angle symbols. The middle trapezoid is formed by two slanting lines from each of the top corners to the base of the rectangle. The angles formed by the two slanted lines, which become the hypotenuse of each right triangle, are labeled from 1 to 8 in clockwise direction starting from the top of the left side.
If m∠8=45° , what equation can you write to find the value of m∠7 ?
Since ∠8 is given as 45 degrees, we can use the fact that the sum of the angles in a triangle is 180 degrees.
In the right triangle containing ∠7 and ∠8, we have:
∠7 + ∠8 + 90 = 180
Substituting the given value, we have:
∠7 + 45 + 90 = 180
Simplifying the equation:
∠7 + 135 = 180
To solve for ∠7, we subtract 135 from both sides:
∠7 = 180 - 135
∠7 = 45
Therefore, the value of ∠7 is 45 degrees.
Together, the measures of ∠B , ∠C , and ∠D equal 180°
. The angles have the following measures: m∠B=25° , m∠C=(3x)° , and m∠D=(3x+5)° . What are the measures of ∠C and ∠D ?(1 point)
Since the measures of ∠B, ∠C, and ∠D together equal 180 degrees, we can write the equation:
m∠B + m∠C + m∠D = 180
Substituting the given values, we have:
25 + 3x + (3x + 5) = 180
Combining like terms, we have:
25 + 6x + 5 = 180
Combining further, we have:
30 + 6x = 180
Subtracting 30 from both sides, we have:
6x = 150
Dividing both sides by 6, we have:
x = 25
Substituting the value of x back into the equations for ∠C and ∠D, we have:
m∠C = 3x = 3(25) = 75
m∠D = 3x + 5 = 3(25) + 5 = 75 + 5 = 80
Therefore, the measure of ∠C is 75 degrees and the measure of ∠D is 80 degrees.
An illustration shows intersecting lines and rays. The resulting angles are labeled. A vertical line is intersected by an upward slanting line from left to right. A downward slanting ray extends from the point where the lines intersect to the bottom right. Starting from the top part of the vertical line, the first angle betwee the vertical line and the slanting line is labeled A. Moving clockwise, next angle is labeled Angle B, then Angle C, then Angle D, and then Angle E. All of the angles have degree signs next to their labels, but they do not have degree measurements.
In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)° . What is the measure of ∠D ?