Answer:
1. a. Q° = 95°
b. a = 20.3; b = 19.3
2. p = 36; q = 14.4
Step-by-step explanation:
Question 1:
Recall: The Exterior Angle Theorem of a Triangle states that the size of the exterior angle of a triangle equals the sum of the two sizes of the two opposite angles of the triangle.
a. Based on the theorem,
Q° = 41° + 54° = 95°
b.
✔️122° = 4a + 2a (exterior angle theorem)
122 = 6a
Divide both sides by 6
122/6 = a
a = 20.3
✔️122° + 3b = 180° (angles on a straight line)
3b = 180 - 122
3b = 58
b = 58/3
b = 19.3
Question 2:
Recall: Opposite angles of a parallelogram are equal while adjacent/consecutive angles are supplementary.
✔️2p + 3p = 180° (adjacent angles)
5p = 180
p = 180/5
p = 36
✔️2p = 5q (opposite angles)
Plug in the value of p
2(36) = 5q
72 = 5q
72/5 = q
q = 14.4
<span>Orthocenter of a triangle is the point of intersection of all the altitudes of the triangle.
in this case, the altitude of XY is XZ, and the altitude of XZ is XY, and the two altitudes meet at the origin.
so in this case, X(0,0) is the orthocenter</span>
7x + 6y < 42
6y < -7x + 42
y < -7/6x + 7
slope = -7/6....y int = (0,7)...x int = (6,0)...it will be a dashed line...shading will be below the line....so start at (0,7)...and since the slope is -7/6...go down 7 spaces and to the right 6 spaces, and keep doing this and u will cross the x axis at (6,0)
7x + 6y > - 42
6y > -7x - 42
y > -7/6x - 7
slope = -7/6...y int = (0,-7)....x int = (-6,0)....line will be dashed....shading will be above the line...so start at (0,-7) and since the slope is -7/6...go down 7 spaces and to the right 6 spaces...keep doing this and u will cross the x axis at (-6,0)
Answer:
x = -5 + y
y = 5 + x
Step-by-step explanation:
Hope this helps!!! :))