Question

The given quadrilateral ABCD is an isosceles trapezoid. Which choice is NOT true about ABCD?

A) 2x + 10 = 4x - 30
B) angle A+ angle B+ angle C+ angle D=180°
C) angle A+ angle B+ angle C+ angle D=360°
D) AB = CD

Solve for angle DAB.
A) 50°
B) 20°
C) 30°
D) 65°

Answer 1

1. b) A + B + C + D = 180°
2. a) 50°

Explanation:

1) Finding the incorrect option?

The incorrect statement is,

→ angle A+ angle B+ angle C+ angle D=180°

(Because, A + B + C + D = 360°)

Hence, option (b) is the answer.

2) Solving for angle DAB?

Forming the equation,

→ 2x + 10 = 4x - 30

Now the value of x will be,

→ 2x + 10 = 4x - 30

→ 2x - 4x = -30 - 10

→ -2x = -40

→ x = -40/-2

→ x = 40/2

→ [ x = 20° ]

Then value of angle DAB is,

→ A = 2x + 10

→ A = 2(20) + 10

→ A = 40 + 10

→ [ A = 50° ]

Hence, option (a) is correct.

Answer 2

• B) angle A+ angle B+ angle C+ angle D=180°
• A) 50°

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Given

• ABCD is an isosceles trapezoid

Solution

Part 1

Choices:

A) 2x + 10 = 4x - 30

• TRUE, as A and D are congruent angles

B) angle A+ angle B+ angle C+ angle D=180°

• NOT true, as the sum of interior angles is 360° not 180°.

C) angle A+ angle B+ angle C+ angle D=360°

• TRUE

D) AB = CD

• TRUE, as marked same.

Part 2

Find the value of x:

• 2x + 10 = 4x - 30
• 4x - 2x = 10 + 30
• 2x = 40
• x = 20

Find the measure of angle DAB:

• m∠DAB = 2*20 + 10 = 50°

Correct choice is A.