In triangle ABD, AC is an altitude, measure of angle 1 = 7x + 9 and measure of angle 2 = 3x + 11. What is the measure of angle 1.
You have to tell us what angles 1 and 2 are, in terms of the points A,B,C,D.
To find the measure of angle 1, we need to set up and solve an equation using the given information in triangle ABD.
We know that angle 1 is the measure of angle BAD, and angle 2 is the measure of angle BAC. Since AC is an altitude, angle 1 and angle 2 are complementary angles. This means that the sum of angle 1 and angle 2 is equal to 90 degrees.
Therefore, we can set up the equation:
angle 1 + angle 2 = 90 degrees
Substituting the given expressions for angle 1 and angle 2, we have:
(7x + 9) + (3x + 11) = 90
Simplifying the equation, we combine like terms:
10x + 20 = 90
Next, we isolate the variable by subtracting 20 from both sides of the equation:
10x = 90 - 20
10x = 70
Finally, we solve for x by dividing both sides of the equation by 10:
x = 70 / 10
x = 7
Now that we have found the value of x, we can substitute it back into the expression for angle 1:
angle 1 = 7x + 9 = 7(7) + 9 = 49 + 9 = 58
Therefore, the measure of angle 1 is 58 degrees.