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3 years ago

Δ ABC is isosceles with m∠B ≅ m∠C. If m∠A = 100°, m∠B = (12x + 4)°, and m∠C = (14x - 2)°, find x.

Mathematics

1 answer:

natita [175]3 years ago

6 0

Answer:

x = 3

Step-by-step explanation:

Since ΔABC is isosceles with ∠A = 100° then the base angles are equal, that is

∠C = ∠B , that is

14x - 2 = 12x + 4 ( subtract 12x from both sides )

2x - 2 = 4 ( add 2 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

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If the measure of angle BCD=51 degrees, solve for x.

BabaBlast [244]

Answer:

$x=5$

Step-by-step explanation:

step 1

Find the measure of angle EFD

In this problem I will assume that ABCD is a parallelogram

In a parallelogram opposite angles are congruent and consecutive angles are supplementary

$m\ angle BCD=m\angle BED=51^o$

$m\ angle FED=(1/2)m\angle BED=(1/2)51^o=25.5^o$ --- > given problem

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

In the triangle EFD

$m\ angle FED+m\ angle FDE+m\ angle EFD=180^o$

substitute the given values

$25.5^o+55^o+m\ angle EFD=180^o$

$80.5^o+m\ angle EFD=180^o$

$m\ angle EFD=180^o-80.5^o$

$m\ angle EFD=99.5^o$

step 2

Find the measure of angle EFB

we know that

$m\angle EFB+m\angle EFD=180^o$ ---> by supplementary angles

we have

$m\ angle EFD=99.5^o$

substitute

$m\angle EFB+99.5^o=180^o$

$m\angle EFB=180^o-99.5^o$

$m\angle EFB=80.5^o$

step 3

Find the value of x

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

In the triangle EBF

$m\ angle BEF+m\ angle EFB+m\ angle EBF=180^o$

we have

$m\angle BEF=m\ angle FED=25.5^o$

$m\angle EFB=80.5^o$

$m\angle EBF=(14x+4)^o$

substitute

$25.5^o+80.5^o+(14x+4)^o=180^o$

solve for x

Combine like terms

$(14x+110)^o=180^o$

$14x=180-110$

$14x=70$

$x=5$

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5(b + 6) = 18
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b = -2.4

answer
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