Answer:
Measurement of each angle of parallelogram is 72⁰, 108⁰, 72⁰ and 108⁰.
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.
[tex]\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 = \dfrac{360}{10}}}}\\\\\quad{\longrightarrow{\sf{x = \dfrac{36 \cancel{0}}{1 \cancel{0}}}}}\\\\\quad{\longrightarrow{\sf{x = {36}^{0}}}}\\\\\qquad{\star{\underline{\boxed{\sf{\purple{x = {36}^{0}}}}}}}\end{gathered}[/tex]
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
[tex]\rule{300}{2.5}[/tex]
