Two angles, ∠1

The sum of the measures of complementary angles is 90 degrees.

So, the equation to solve for m∠1 can be written as:

m∠1 + m∠2 = 90°

Substituting the given information, we have:

m∠1 + 26° = 90°

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 ?

Vertical angles are congruent, and supplementary angles add up to 180 degrees.

So, the equation to solve for m∠4 can be written as:

m∠3 = m∠4

m∠4 + m∠5 = 180°

Substituting the given information, we have:

67° = m∠4

Use the image to answer the question.

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 ?

In a rectangle, opposite angles are congruent.

Therefore, we have:

m∠7 = m∠5

Since m∠8 = 45°, and the sum of the angles in a triangle is 180°, we know that:

m∠7 + m∠8 + m∠5 = 180°

Since we already know that m∠8 = 45°, we can substitute this value into the equation:

m∠7 + 45° + m∠5 = 180°

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 ?
m∠C=
°

m∠D=
°

Given that the measures of ∠B, ∠C, and ∠D add up to 180°, 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:

25 + 6x + 5 = 180

30 + 6x = 180

Subtracting 30 from both sides:

6x = 150

Dividing both sides by 6:

x = 25

So, m∠C = (3x) = 3(25) = 75°.

And, m∠D = (3x + 5) = (3(25) + 5) = 75 + 5 = 80°.

Therefore,

m∠C = 75°

m∠D = 80°

Find Missing Angles Practice

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5 of 55 of 5 Items

Question
Use the image to answer the question.

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 ?

The measure of ∠D is given as (2x+22)°.

Since we are not given any specific information or equation relating angle measures, we cannot determine the specific value of ∠D. We would need additional information or equations to solve for x and find the specific measure of ∠D.

Question

Use the image to answer the question.

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 ?

The measure of ∠D is given as (2x+22)°.

To find the measure of ∠D, we can set up an equation based on the information given.

Since the angles formed by intersecting lines are supplementary, we can write:

m∠A + m∠D = 180°

Substituting the given values:

(4x-10) + (2x+22) = 180

Combining like terms:

6x + 12 = 180

Subtracting 12 from both sides:

6x = 168

Dividing both sides by 6:

x = 28

Now that we know the value of x, we can substitute it back into the expression for ∠D:

∠D = 2x + 22
∠D = 2(28) + 22
∠D = 56 + 22
∠D = 78°

Therefore, the measure of ∠D is 78°.