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3 years ago

How do you solve this?

Mathematics

1 answer:

Rus_ich [418]3 years ago

4 0

Answer:

x=25°, y=10°

Step-by-step explanation:

∠A+∠B=180°

8y+10y=180°

18y=180°

y=10°

∠B+∠C=180°

10y+4x-20°=180°

10*10°+4x=180°+20° (y=10°)

100°+4x=200°

4x=200°-100°

4x=100°

x=25°

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Find the measure of the the sides of DEF then classify it by it sides. <br> D(8,-6) E(-1,-3) F(-2,5)

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Answer:

Part a) The measure of the sides of triangle DEF are

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

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Part b) Is a scalene triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the coordinates

D(8,-6) E(-1,-3) F(-2,5)

step 1

Find the length side DE

D(8,-6) E(-1,-3)

substitute in the formula

$d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}$

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step 2

Find the length side EF

E(-1,-3) F(-2,5)

substitute in the formula

$d=\sqrt{(5+3)^{2}+(-2+1)^{2}}$

$d=\sqrt{(8)^{2}+(-1)^{2}}$

$d_E_F=\sqrt{65}\ units$

step 3

Find the length side DF

D(8,-6) F(-2,5)

substitute in the formula

$d=\sqrt{(5+6)^{2}+(-2-8)^{2}}$

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step 4

Classify the triangle by the measure of its sides

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$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

Is a scalene triangle, because is a triangle in which all three sides have different lengths.

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3 years ago

Write a two-column proof. Given: line BD bisects angle CBE. Prove: angle ABD approximately equal to angle FBD.

ale4655 [162]

Answer:

The proof is derived from the summarily following equations;

∠FBE + ∠EBD = ∠CBA + ∠CBD

∠FBE + ∠EBD = ∠FBD

∠CBA + ∠CBD = ∠ABD

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∠ABD ≅ ∠FBD

Step-by-step explanation:

The two column proof is given as follows;

Statement ${}$ Reason

$\underset{BD}{\rightarrow}$ bisects ∠CBE ${}$ Given

Therefore;

∠EBD ≅ ∠CBD ${}$ Definition of angle bisector

∠FBE ≅ ∠CBA ${}$ Vertically opposite angles are congruent

Therefore, we have;

∠FBE + ∠EBD = ∠CBA + ∠CBD ${}$ Transitive property

∠FBE + ∠EBD = ∠FBD ${}$ Angle addition postulate

∠CBA + ∠CBD = ∠ABD ${}$ Angle addition postulate

Therefore;

∠ABD ≅ ∠FBD ${}$ Transitive property.

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