ABCD diagonals intersect at E. If m∠BAC=4x+5 and m∠CAD=5x-14, then find m∠CAD.
1 answer:
Answer: m∠CAD = 81°
Step-by-step explanation: <u>Diagonal</u> is a line that unites opposite sides.
ABCD is a prallelogram. One property of diagonal in a parallelogram is it separates the parallelogram in 2 congruent triangles.
The figure below shows ABCD with its diagonals.
Since diagonal divides a parallelogram in 2 congruent triangles, it means the internal angles are also congruent. So
m∠BAC = m∠CAD
4x + 5 = 5x - 14
x = 19
Then, m∠CAD is
m∠CAD = 5(19) - 14
m∠CAD = 81
The angle m∠CAD is 81°.
You might be interested in
Answer:
y = -2x + 9
Step-by-step explanation:
The parallel line has an equation of y = -2x + 7;
And its slope is -2.
The slope of the line that passes through (4,1) is also -2 since parallel lines have the same slope.
Taking another point (x,y) on the line that passes through (4,1):
slope(m) = change in y ÷ change in x
-2 =
Cross multiplying gives;
y - 1 = -2x + 8
y = -2x + 9