Answer:
70°
Step-by-step explanation:
The total angle in a triangle is 180°. The total angle in a straight line is 180°. From the image attached, the ∠DCA must be greater than 45° because ∠BCA is greater than 90°. This means that ∠DCA is not 36° or 38° or 40° but it is 70°.
Therefore ∠DCA = 70°.
∠BCA + ∠DCA = 180° (angle on a straight line)
∠BCA = 180 - ∠DCA = 180 - 70 = 110°
∠BCA + ∠BAC + 40 = 180° (angle in a triangle)
∠BAC = 180 - 110 - 40 = 30°
Answer:
1) y=⅚x -2⅓
2) y=8/3x -5
Step-by-step explanation:
<u>Point-slope form:</u>
y=mx+c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient.
Gradient of given line=
Thus, m=⅚
Susbt. m=⅚ into the equation,
y= ⅚x +c
Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.
When x=4, y=1,
1= ⅚(4) +c
Thus the equation of the line is .
The gradients of perpendicular lines= -1.
Gradient of given line= -⅜
-⅜(gradient of line)= -1
gradient of line
= -1 ÷ (-⅜)
= -1 ×(-8/3)
=
When x=3, y=3,
Thus the equation of the line is .