Question

The consecutive angles of a parallelogram measure $(x°+{30}^{\circ })$ and $4x°$. What is the measure of the smallest angle?

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${40}^{\circ }$
• D. ${10}^{\circ }$

Answer 1

The correct option is B

${60}^{\circ }$

Explanation for the correct option:

Option(B):

Find the measure of the smallest angle:

Given that, the consecutive angles of a parallelogram measure $(x°+{30}^{\circ })$ and $4x°$.

In a parallelogram, the sum of the consecutive angles is ${180}^{\circ }$

Step-1: Find the value of $\mathbf{x}\mathbf{°}$:

Equate, the sum of the given angle measure $(x°+{30}^{\circ })$ and $4\mathrm{x}°$ with ${180}^{\circ }$ to find $\mathrm{x}°:$

$$\begin{gathered} \Rightarrow x°+{30}^{\circ }+4x°={180}^{\circ } \\ \Rightarrow 5x°+{30}^{\circ }={180}^{\circ } \\ \Rightarrow 5x°={180}^{\circ }-{30}^{\circ } \\ \Rightarrow 5x°={150}^{\circ } \\ \Rightarrow x°=\frac{{150}^{\circ }}{5^{\circ }} \\ \Rightarrow x°={30}^{\circ } \end{gathered}$$
Step- 2: Find the measure of the smallest angle:

Substitute $x={30}^{\circ }$in $(x+{30}^{\circ })$ and then $4x:$
$\begin{array}{rcl}(x°+{30}^{\circ })& =& {30}^{\circ }+{30}^{\circ }\\ & \Rightarrow & ={60}^{\circ }\\ 4(x°)& =& 4\left({30}^{\circ }\right)\\ & \Rightarrow & ={120}^{\circ }\end{array}$

So, from these two angles of a parallelogram, the smallest measure is ${60}^{\circ }.$

As it has been found that for the given parallelogram angle measure, the smallest measure is an option (B) ${60}^{\circ }$, so, the remaining options of Option (A) ${30}^{\circ }$, Option (C)${40}^{\circ }$ and Option (D) ${10}^{\circ }$are incorrect answers.

Hence, for the consecutive angles of a parallelogram measure $(x+{30}^{\circ })$ and $4\mathrm{x}$, the measure of the smallest angle is ${60}^{\circ }$which is an option (B).

Hence, option (B) is correct answer.