Question

Please help me solve this math problem im in desperate need

Answer 1

Measurement of each angle of parallelogram is 72⁰, 108⁰, 72⁰ and 108⁰.

Step-by-step Step-by-step explanation:

Let the angle measurement of parallelogram be 2x, 3x, 2x, 3x.

• As we know that, the sum of interior angles of parallelogram is 360⁰.

Now, according to the question substituting all the given values to find the value of x.

`\begin{gathered} \qquad{\longrightarrow{\sf{2x + 3x + 2x + 3x = {360}^(0)}}}\\\\ \qquad{\longrightarrow{\sf{5x + 2x + 3x = {360}^(0)}}}\\\\\quad{\longrightarrow{\sf{7x + 3x = {360}^(0)}}} \\ \\ \quad{\longrightarrow{\sf{10x = {360}^(0)}}}\\\\\quad{\longrightarrow{\sf{x = (360)/(10)}}}\\\\\quad{\longrightarrow{\sf{x = \frac{36 \cancel{0}}{1 \cancel{0}}}}}\\\\\quad{\longrightarrow{\sf{x = {36}^(0)}}}\\\\\qquad{\star{\underline{\boxed{\sf{\purple{x = {36}^(0)}}}}}}\end{gathered}`

Hence, the value of x us 36⁰.

Now, we know the value of x. So, calculating the measurement of each angle of parallelogram :

• 2x = 2 × 36 = 72⁰
• 3x = 3 × 36 = 108⁰
• 2x = 2 × 36 = 72⁰
• 3x = 3 × 36 = 108⁰

`\rule{300}{2.5}`