Find the measure of each angle if <BAD and <BDC are right angles and m<ABC=84
I assume you are working with a quadrilateral ABCD in which angles BAD and BCD are right angles.
Since the four interior angles of a quadrilateral add up to 360°, therefore the remaining angles add up to (360-90-90)=180°.
Can you figure out the fourth angle now?
Your mom
To find the measure of each angle, we can start by using the fact that angles BAD and BDC are right angles. In a right triangle, one of the angles is always 90 degrees.
So, angle BAD = 90 degrees.
Next, we can use the fact that angle ABC is 84 degrees to find the measure of angle BAC. In a triangle, the sum of the interior angles is always 180 degrees.
m<ABC + m<BAC + m<ACB = 180 degrees
Substituting the given values, we get:
84 + m<BAC + 90 = 180
Now, we can solve for m<BAC:
m<BAC = 180 - 84 - 90
= 6 degrees
So, angle BAC = 6 degrees.
Finally, to find the measure of angle ACB, we can use the fact that the sum of the interior angles in a triangle is always 180 degrees:
m<BAC + m<ABC + m<ACB = 180 degrees
Substituting the given values, we get:
6 + 84 + m<ACB = 180
Now, we can solve for m<ACB:
m<ACB = 180 - 6 - 84
= 90 degrees
Therefore, angle ACB = 90 degrees.
In summary, the measure of each angle is as follows:
- Angle BAD = 90 degrees
- Angle BAC = 6 degrees
- Angle ACB = 90 degrees