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
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
[tex]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.[/tex]
Thus, the required value of x is 15.
Option (A) is CORRECT.
