1. in ∆abc the angle bisectors drawn from vertexes a and b intersect at point d. find ∠adb if: m∠a = α , m∠b = β 2.angle bisectors of the angles ∠a and ∠b of a triangle ∆abc intersect each other at point m. find m∠amb, if m∠a = 58°, m∠b = 96°.

Answer (1)

As given in question

In ∆ABC,  angle bisectors drawn from vertexes A and B intersect at point D

m∠A = α , m∠B = β

Find ∠ADB

To proof

As shown in the diagram given below

AE and BF is angle bisector.

( angle bisector are the bisector which divided angle in two equal parts )

m∠A = α , m∠B = β   ( given)

Thus

Now in ΔADB

∠ADB +∠ BAD +∠ ABD = 180 °

( Angle sum property of a triangle )

Hence proved

ANSWER (2)

.Angle bisectors of the angles ∠A and ∠B of a triangle ∆ABC intersect each other at point M.

m∠A = 58°, m∠B = 96°

Find m∠AMB

To proof

As shown in the diagram given below

AE and BF is angle bisector

∠BAM = 29°

∠ABM = 48°

InΔAMB

∠AMB +∠BAM +∠ABM = 180°

( Angle sum property of a triangle)

putting the value

we get

∠AMB = 180 - 48 - 29

∠AMB = 103 °

Hence proved

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles

answer:

total cost for tiles and paints is $924.  

step-by-step explanation:

we have been given that a community hall is in the shape of a cuboid. the hall is 40m long 15m high and 3m wide.

the paint will be required for 4 walls and ceiling.

let us find area of walls and ceiling.

therefore, the area of walls and ceiling is 1410 square meters.

given: cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter. therefore,

therefore, the total painting cost is $564.

tiles will be required for floor. let us find the area of floor.

given: 1m squared floor tiles costs $3. so,

therefore, the total tiles cost is $360.

now let us find combined total cost of tiles and paint.

therefore, the combined total cost of tiles and paint is $924.