ABCD is an isosceles trapezoid with AD II BC, mZB = 60°, and mZC = (3x +15) Solve for x.

Mathematics

2 answers:

Gnesinka [82]4 years ago

8 0

Answer:

A 15

Step-by-step explanation:

In an isosceles trapezoid, each pair of base angles is congruent.

In this isosceles trapezoid, angles B and C are congruent, so their measures are equal.

m<B = m<C

60 = 3x + 15

Subtract 15 from both sides.

45 = 3x

Divide both sides by 3.

15 = x

x = 15

Wewaii [24]4 years ago

4 0

Answer: The correct option is (A) 15.

Step-by-step explanation: As shown in the attached figure below, ABCD is an isosceles trapezoid with AD parallel to BC.

Also, m∠B = 60° and ∠C = (3x +15)°.

We are to find the value of x.

Since ABCD is an isosceles trapezoid with AB and CD as the two legs, so we have

$AB=CD\\\\\Rightarrow m\angle C=m\angle B~~~~~~~~~~~~~~~~~~~[\textup{Angles opposite to equal legs are equal}]\\\\\Rightarrow (3x+15)^\circ=60^\circ\\\\\Rightarrow 3x+15=60\\\\\Rightarrow 3x=60-15\\\\\Rightarrow 3x=45\\\\\Rightarrow x=\dfrac{45}{3}\\\\\Rightarrow x=15.$