46° 7 8
T
E
8
15
10
6
29°
S
20
Given ASTU and ADEF,
what is mZD? what is m/T?
Please help

m ∠D = 29°

m ∠T  = 105°

Step-by-step explanation:

Given: ΔSTU and ΔDEF

To find: m ∠D and m ∠T

Solution:

According to SSS similarity criteria,

two triangles are said to be similar if their corresponding sides are proportional.

In ΔSTU and ΔDEF,

So,

Therefore,

ΔSTU ≈ ΔDEF

If two triangles are similar then measure of their corresponding angles are equal.

m ∠D = m ∠S = 29°

m ∠U = m ∠F = 46°

In ΔSTU,

m ∠S + m ∠T + m ∠U = 180°

29° + m ∠T + 46° = 180°

75° + m ∠T = 180°

m ∠T  = 180° - 75° = 105°

(According to angle sum property of a triangle, sum of measures of angles of a triangle is equal to 180°)

dhdhth

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."