Question

the sum of the interior triangle measures of a quadrilateral is 360 degrees. the measure of angle A is three times the measure of angle D. The measure of angle B is four times that of angle D. The measure of angle C is 24 degrees more than angle B. FInd the measure of each triangle

Answer 1

The measure of angle A is 84 degrees, angle B is 112 degrees, angle C is 136 degrees, and angle D is 28 degrees.

Step-by-step explanation:

Let's denote the measures of angles A, B, C, and D as A°, B°, C°, and D°, respectively.

We are given that the sum of the interior triangle measures of the quadrilateral is 360 degrees. Since a quadrilateral has four angles, we can represent this as:

A° + B° + C° + D° = 360

From the given information, we have:

A° = 3D°

B° = 4D°

C° = B° + 24°

Substituting these values into the equation, we get:

3D° + 4D° + (4D° + 24°) + D° = 360

Simplifying this equation gives:

12D° + 24° = 360

Subtracting 24° from both sides:

12D° = 336

Dividing both sides by 12:

D° = 28

Now we can find the measures of the other angles:

A° = 3D° = 3(28) = 84

B° = 4D° = 4(28) = 112

C° = B° + 24° = 112 + 24 = 136

Therefore, the measure of angle A is 84 degrees, angle B is 112 degrees, angle C is 136 degrees, and angle D is 28 degrees.

Answer 2

Step-by-step explanation:

The sum of the measures of the interior angles of any quadrilateral can be found by breaking the quadrilateral into 2 triangles.

Since, the measure of the interior angles of any triangle equals 180 degrees,

a+b+c=180

p+q+r=180

Each of the two triangles will contribute 180 degrees to the total for the quadrilateral.

Sum of angles of quadrilateral

= b+(a+p)+q+(r+c)=a+b+c+p+q+r=180+180

=360=4×90

=4 right angles