An equilateral triangle and an isosceles triangle share a common side. what is the measure of angle abc?

Therefore ,the measure of angle ABC = 116°.

Step-by-step explanation:

Given:

Δ CBD is an Equilateral Triangle

BC = BD = CD

Δ ABD is an Isosceles Triangle

AB = BD

To Find:

m∠ ABC = ?

Solution:

Property For an Equilateral Triangle:

All the measure of Each of the angles angles of a triangle is 60°.

Δ CBD is an Equilateral Triangle   Given

∴ m∠ CBD = 60° ( 1 )

Property For an Isosceles Triangle:

Any two of the base angles are equal.

Δ ABD is an Isosceles Triangle Given

∴ m∠ BAD = m∠ BDA = 62°  ( 2 )

Property of Triangle:

SUM of the measure of an angles of a triangle is 180°

In Δ BAD,

m∠ ABD + m∠ BAD + m∠ BDA = 180°

Substituting the values from equation ( 2 ) in it we get

m∠ ABD + 62 + 62 = 180

∴ m∠ ABD = 180 -124

∴ m∠ ABD = 56°     ( 3 )

Now By angle addition property we have

m∠ ABC = m∠ ABD  + m∠ CBD

Substituting the values from equation 1 and equation 3 we get

∴ m∠ ABC = 56 + 60

∴ m∠ ABC = 116°

Therefore ,the measure of angle ABC = 116°.

(x+3)(x+7)

step-by-step explanation:

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

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