Rays AB and BC are perpendicular. Point D lies in the interior of angle ABC. If m angle ABD = 3r+5 and m angle DBC= 5r-27, find m angle ABD ana m angle DBC.

(3r+5) + (5r-27) = 90

8r - 22 = 90
8r = 112
8r/8 = 112/8
r = 14

<DBC = 5(14) - 27
<DBC = 43

(3r+5)+(5r-27)=90 8r-22=90 8r=90+22 8r÷8=112 ÷8 r=14. ABD= 3r+5 ABD=3(14)+5 ABD=42+5 ABD=47. DBC =5r-27 DBC=5(14)-27 DBC=70-27 DBC=43. The end!

WX and YZ intersect at point V. If mZWVY = (40 + 58)° and m/XVY = (26 - 18)°, find the values of a and b such that WX is perpendicular to YZ.

Well, if we have a triangle ABC where AB and BC are perpendicular, it means that angle ABC is a right angle, right? So, since point D lies in the interior of angle ABC, it means that angles ABD and DBC must add up to 90 degrees.

Now, let's use some algebraic clownery to find the values of angles ABD and DBC. We have m angle ABD = 3r + 5 and m angle DBC = 5r - 27. By setting their sum equal to 90 degrees, we get:

(3r + 5) + (5r - 27) = 90

Combine like terms:

8r - 22 = 90

Now, let's isolate r by adding 22 to both sides:

8r = 112

And divide both sides by 8:

r = 14

Now that we know r is equal to 14, we can substitute this value back into the expressions for angles ABD and DBC:

m angle ABD = 3(14) + 5 = 42 + 5 = 47 degrees

m angle DBC = 5(14) - 27 = 70 - 27 = 43 degrees

So, the measure of angle ABD is 47 degrees and the measure of angle DBC is 43 degrees. Voila!

To find the measures of angles ABD and DBC, we will use the properties of perpendicular lines and angles.

Given:
- Rays AB and BC are perpendicular.
- Point D lies in the interior of angle ABC.
- The measure of angle ABD is 3r + 5.
- The measure of angle DBC is 5r - 27.

To find the measures of angles ABD and DBC, we need to set up an equation using the properties of perpendicular lines.

When two lines are perpendicular, the adjacent angles formed are complementary, which means their measures add up to 90 degrees.

In this case, angles ABD and DBC are adjacent angles formed by the perpendicular rays AB and BC. Therefore, we can set up the equation:

m angle ABD + m angle DBC = 90 degrees

Substituting the values given:

(3r + 5) + (5r - 27) = 90

Simplifying the equation:

8r - 22 = 90

Adding 22 to both sides:

8r = 112

Dividing both sides by 8:

r = 14

Now that we have found the value of r, we can substitute it back into the expressions for the measures of angles ABD and DBC to find their values.

m angle ABD = 3r + 5 = 3(14) + 5 = 42 + 5 = 47 degrees

m angle DBC = 5r - 27 = 5(14) - 27 = 70 - 27 = 43 degrees

Therefore, the measure of angle ABD is 47 degrees and the measure of angle DBC is 43 degrees.

Hsgf

ABD+DBC = ABC so

3r+5 + 5r-27 = 90
r = 14
Now finish it off