What is the area of a regular pentagon with a side length of 7 feet and a length from the center to a vertex of 6 feet?
2 answers:
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Given that a || b, m∠2 = 63° and m∠9 = 105°.
Now, all the angles are as follows:
m∠5= m∠2 = 63° [vertically opposite angle]
m∠7= m∠9=105° [vertically opposite angle]
m∠8= 180°-m∠9=180°-105°=75° [Supplementry angles, m∠8+m∠9=180°]
m∠10= m∠8= 180° [vertically opposite angle]
m∠6= m∠8=75° [ Alternate angles]
m∠3= m∠6=75° [vertically opposite angle]
m∠1= 180°-(m∠2+m∠3)=180°-(63°+75°)=42° [as m∠1+m∠2+m∠3=180°]
m∠4= m∠1=42° [vertically opposite angle]
m∠11=m∠4=42° [ Alternate angles]
m∠13= m∠11=42° [vertically opposite angle]
m∠12= 180°-m∠11=180°-42°=138° [as m∠8+m∠9=180°]
m∠14 = m∠12=138° [vertically opposite angle]
Answer:
Step-by-step explanation:
<u>Right Triangles</u>
Right triangles have one of its interior angles with a measure of 90°.
In right triangles the Pythagora's Theorem is satisfied.
Being c the longest side (hypotenuse), a and b the shorter sides (the legs), then:
We have modified the image to include some known data. Both triangles are congruent since they share one side, have a right angle, and have the same base length.
This means the value of x can be calculated as the hypotenuse of the triangle 3-6-x: