Question

question 12 of 27
find the value of x that makes abcd a parallelogram.
diagram of parallelogram abcd with angles: ∠a = 70°, ∠b = x + 60°, ∠c = 70°, ∠d = x + 60°
a. x = 40°
b. x = 30°
c. x = 50°
d. x = 10°

Explanation:

Step1: Recall parallelogram angle property

In a parallelogram, consecutive angles are supplementary (sum to \(180^\circ\)). So, \(\angle A + \angle B = 180^\circ\).
Given \(\angle A = 70^\circ\) and \(\angle B = x + 60^\circ\), we have the equation:
\(70^\circ + (x + 60^\circ) = 180^\circ\)

Step2: Solve for \(x\)

Simplify the left - hand side: \(70 + x + 60 = 130 + x\)
So the equation becomes \(130 + x = 180\)
Subtract \(130\) from both sides: \(x = 180 - 130\)
\(x = 50^\circ\) (Wait, no, wait. Wait, maybe I made a mistake. Wait, in a parallelogram, opposite angles are equal, and consecutive angles are supplementary. Wait, let's check again. Wait, \(\angle A\) and \(\angle C\) are equal (\(70^\circ\) each), \(\angle B\) and \(\angle D\) are equal (\(x + 60^\circ\) each). Also, consecutive angles: \(\angle A\) and \(\angle B\) should be supplementary. So \(\angle A+\angle B = 70+(x + 60)=180\). So \(x+130 = 180\), so \(x = 50\)? But wait, let's check the options. Wait, option C is \(x = 50^\circ\)? Wait, no, wait, maybe I messed up. Wait, no, let's re - examine. Wait, maybe the angles at \(A\) and \(B\) are consecutive. So \(70+(x + 60)=180\). So \(x=180 - 130 = 50\). But wait, let's check the options. Option C is \(x = 50^\circ\). Wait, but let's check again. Wait, maybe the problem is that in a parallelogram, adjacent angles are supplementary. So angle \(A\) is \(70^\circ\), angle \(B\) is \(x + 60^\circ\). So \(70+(x + 60)=180\). So \(x=180 - 130 = 50\). So the answer should be C? Wait, but let's check the options again. The options are A. \(40\), B. \(30\), C. \(50\), D. \(10\). So according to this, \(x = 50^\circ\), which is option C. Wait, but maybe I made a mistake. Wait, let's check the angle sum. In a quadrilateral, the sum of interior angles is \(360^\circ\). In a parallelogram, opposite angles are equal. So \(\angle A=\angle C = 70^\circ\), \(\angle B=\angle D=x + 60^\circ\). So total sum: \(2\times70+2\times(x + 60)=360\). Divide both sides by 2: \(70+(x + 60)=180\), which is the same as before. So \(x + 130 = 180\), so \(x = 50\). So the correct answer is C.

Answer:

C. \(x = 50^\circ\)