13 POINTS FOR ANSWERS TO ALL STEPS
geometry triangles

Step-by-step explanation:

a) We know that triangle ABD is a right triangle, because of the right angle mark show, and the fact that BD- height, thus perpendicular.

We also know that m<A=30 degrees, due to given diagram.

The sum of all angles in a triangle is 180 degrees. Therefore, m<BDA + m<ABD + m<DAB (Usain Bolt!) = 180 degrees.

m<BAD=30 degrees, m<BDA=90 degrees

Substitute these two in the equation above. You will get that m<ABD=60 degrees.

b) Triangle ABD is a special triangle, with angles of 30,60 and 90.

We know that AD=10 units.

AD is opposite the 60 degree angle, or <ABD. It is a theorem that the angle opposite to the 60 degree angle is the height (BD) divided by . Calculate, and what do you get? BD=10 units!

c) Use the fact that triangle ABC is an isosceles triangle.

d) Use the fact that you know the height, base, and triangle area formula: Base x 1/2 x Height.

I will say no more, but I hope you understand the rest based on your logic.

5. <ABC & ECB 6. 180-degrees

Step-by-step explanation:

If triangle CDA is triangle ABC after a 180-degree rotation then ABC would be equal to ECB.

As for problem number 6, all the angles fit into a perfect line. The angle of a line is 180-degrees. Therefore if you added them all together it would equal 180.