MATHEMATICS HIGH SCHOOL

An angle measures 142° less than the measure of its supplementary angle. What is the measure of each angle?
An angle measures 142° less than the measure of its - 1

Answers

Answer 1
Answer:

Answer:

              19° and 161°

Step-by-step explanation:

A - an angle

S - its suplementary angle

A = S - 142°

Suplementary angles add to 180° so:

A + S = 180°

S - 142° + S = 180°

2S  = 322°

S = 161°

A = 161° - 142° = 19°

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Answers

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ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?

Answers

Given : - Square ABCD with side 3.  E and F as midpoints.
To find : - area of EBFD

Solution : - We have, area of square ABCD = 3 x 3 = 9 units.

Thus, (ar)EBFD = ar ABCD - ar DAE - arDCF

arDAE = 1/2 x base x height

=1/2 x 1.5 x 3 ( AE is 1/2 of AB = 1.5, DA is altitude)
= 2.25

arDFC = 1/2 x base x height 
= 1/2 x 1.5 x 3 (FC is 1/2 of BC, DC is altitude)
= 2.25

Thus, (ar) EBFD = arABCD - arDAE - arDCF

= 9 - 2.25 - 2.25

= 4.5 units.

Thus, area of quad EBFD is 4.5 units.  

What is the measure of DC

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