Question

1. a pendant flag is made up of a stick and a triangular flag, as shown in the diagram below. what is, n, the total height in inches of the stick?10 in8 in14 inabcd7.115°140°abcd8.given that lines a and b are parallel and that m∠1=128°. find m∠5a1 23 4b5 67 8a 32°b 52°c 82°d 90°e 128°9.given that m∠4=140°, find m∠61 23 45 67 8a 40°b 80°c 130°d 140°e 160°

Explanation:

Step1: Solve for triangular segment height

Use Pythagorean theorem: $a^2 + b^2 = c^2$. Let the vertical segment of the triangle be $x$.
$x^2 + 8^2 = 10^2$
$x^2 = 100 - 64 = 36$
$x = \sqrt{36} = 6$

Step2: Calculate total stick height

Add the triangular segment height to the lower stick length.
$h = 6 + 14 = 20$

Step1: Find adjacent triangle angle

The 140° angle is supplementary to the triangle's base angle.
$180^\circ - 140^\circ = 40^\circ$

Step2: Solve for unknown angle $x$

Triangle angles sum to $180^\circ$.
$x = 180^\circ - 110^\circ - 40^\circ = 30^\circ$

Step1: Identify angle relationship

$\angle 1$ and $\angle 5$ are corresponding angles (parallel lines cut by transversal), so $\angle 1 = \angle 5 = 128^\circ$.

Step2: Verify supplementary pair

$\angle 5$ and $\angle 6$ are supplementary.
$\angle 6 = 180^\circ - 128^\circ = 52^\circ$

Step1: Identify vertical angle

$\angle 4$ and $\angle 2$ are vertical angles, so $\angle 2 = \angle 4 = 140^\circ$.

Step2: Identify corresponding angle

$\angle 2$ and $\angle 6$ are corresponding angles (parallel lines cut by transversal), so $\angle 6 = \angle 2 = 140^\circ$.

Answer:

D. 20

---