Question

What is the measure of the smaller angle in the rhombus below?

Answer 1

Answer:

x= 22

Step-by-step explanation:

x+14=2x-8

14+8=2x-x

x=22

Answer 2

The smallest angle of rhombus is 72°.

Given:

• A figure.

To find:

• What is the measure of the smaller angle in the rhombus.

Solution:

Concept/formula to be used:

• The opposite angles of rhombus are equal.
• The sum of all interior angles of the rhombus is 360°.

Step 1:

Write the angle measure of rhombus.

According to the property of rhombus,

$\bf \angle A=\angle C = x + {14}^{ \circ}$

$\bf \angle B=\angle D= 2x - {8}^{ \circ}$

Step 2:

Find the smallest angle of rhombus.

$\bf \angle A + \angle B + \angle C + \angle D = {360}^{ \circ}$

$\angle A + \angle B + \angle C + \angle D = 2(x + {14}^{ \circ}) + 2(2x - {8}^{ \circ} )$

$2(x + {14}^{ \circ}) + 2(2x - {8}^{ \circ} ) = {360}^{ \circ}$

$2x + {28}^{ \circ} + 4x - {16}^{ \circ} = {360}^{ \circ}$

$6x + {12}^{ \circ} = {360}^{ \circ}$

$6x = {360}^{ \circ} - {12}^{ \circ}$

$x = \frac{348^{\circ}}{6}$

$\bf x = {58}^{ \circ}$

The smallest angle of rhombus is $x + {14}^{ \circ} = {58}^{ \circ} + {14}^{ \circ}$

$\bf \angle A=\angle C\: = {72}^{ \circ}$

Thus,

The smallest angle of rhombus is 72°.

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