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2 years ago

A map

Mathematics

1 answer:

Bess [88]2 years ago

6 0

The scale of the map from inches to miles is 1 inch : 9 miles

<h3>How to determine the scale of the map from inches to miles?</h3>

The given parameters are:

The actual distance of the cities apart = 36 miles
The scale distance of the cities apart = 4 inches

The scale of the map from inches to miles is represented as:

Scale of map = The scale distance of the cities apart : The scale distance of the cities apart

Substitute the known values in the above equation

Scale of map = 4 inches : 36 miles

Divide both sides of the ratio by 4

So, we have:

Scale of map = 4/4 inches : 36/4 miles

Evaluate the quotient

Scale of map = 4/4 inches : 9 miles

Evaluate the quotient

Scale of map = 1 inch : 9 miles

Hence, the scale of the map from inches to miles is 1 inch : 9 miles

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19. Given that angle BFC = 58°. Angle BXG = 48° and angle CBF 22 Find () 2BGX (iv) BCG (i) 2BGF (iv) ZBFG (ii) BCF H EE 58 48° D

RoseWind [281]

The unknown angles in the cyclic quadrilateral is as follows:

∠BGX = 74° (sum of angles in a triangle)

∠BGF = 180° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 100°(sum of angles in a triangle)

∠BCG = 26°

∠BFG = 22°

<h3>Cyclic Quadrilateral</h3>

A cyclic quadrilateral has all its angles equal to 360 degrees. The sum of angles in a cyclic quadrilateral is equals to 360 degrees.

Let's find the missing angles as follows:

∠BGX = 180 - 48 - 58 = 74° (sum of angles in a triangle)

∠BGF = 180 - 100 = 80° (opposite angles of cyclic quadrilateral are supplementary)

∠BCF = 180 - 22 - 58 = 100°(sum of angles in a triangle)

∠BCG = 100 - 74 = 26°

∠BFG ≅ CBF = 22°(alternate angles)

learn more on angles here: brainly.com/question/19430381

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