Geometry Questions and Answers

Let the measure of angle P be P, and the measure of angle Q be Q.

P = 2Q

Given that angles P and Q are complementary. Therefore,

P + Q = 90⁰

But, P = 2Q. Therefore,

2Q + Q = 90

3Q = 90

Q= 90/3 = 30⁰

P =2Q = 60^°

To calculate the measure of angle A, we have to calculate the value of angle B.

Angle B = 180-130= 50⁰

Therefore, the measure of angle A = 180 – (50+60)

A = 180-110

A =70^°

The sum of all the angles in the given triangle ABC is 180⁰

180 = 60 + 90 + BCA

Therefore, angle BCA = 180-150= 30⁰

Angle APC = 60 + 45- 180

180-105 = 75°

From the given figure, angle DEB = 180-120 = 600

Therefore, angle AED = 180-30 = 120°

The internal angle B in the given triangle = 180-130 = 50⁰

The internal angle C in the given triangle = 180-140 = 40⁰

Therefore, in the given triangle, measure of angle A = 180 – (40 + 50)

180 – 90 = 90°

In the given triangle ACE, vale of angle AEC = 180- (60+40)

= 180 – 100

=800

Also, the given angle DEB = 800 as it is directly opposite to angle AEC.

= In triangle DEB, value of angle EDB = 180 – (80+50)

=180 – 130

50°

In the given triangle ABC, value of angle C = 180 – (60+90)

180 – 150 = 30⁰

Now, in the given triangle PCR, value of angle R = 90⁰

Value of angle CPR = 180 – (90+30)

180 – 120 = 60^°

Now, value of angle RPB = (180 - 60) = 120⁰

Area of ABDEF = area of ACEF – area of triangle BCD

= 50 x 30 – ((1/2)*15*25)

= 50 x 30 – 187.5

= 1500 – 187.5

= 1312.5 cm2

The presented figure can be divided into two triangles to calculate the area.

We can also label the given figure to identify and mark the 2 triangles.

Now the figure consists of triangles: ADC and triangle ACB.

The area of the given triangle can be calculated when we know the measure of length AC.

For this, in the given triangle, ADC,

AC² = AD² + DC²

AC² = 20² + 20²

AC =√400+400

AC = √800

AC = 28.28

Area of triangle ADC = ½*20*20

= 200 cm²

We also need the area of the triangle ABC

Area of the triangle when its three sides are given = √p(p-a)(p-b)(p-c)

Where p = (a+b+c)/2

P = (25+5+28.28)/2 = 29.14

Therefore, area of triangle = √29.14(29.14-25)(29.14-5)(29.14-28.28)

= √115.08

= 10.72 cm²

The solution is to rotate the triangle to bring the 10 feet side at the bottom.

<img class="alignnone size-full wp-image-274642" src="https://files.prepinsta.com/wp-content/uploads/2019/11/q10A.png" alt="" width="423" height="231" />

Therefore, the area of the triangle =

Area=

= 25cm²

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