Question

The measures of two consecutive angles of a parallelogram are (3x + 10°) and
(4x + 30)° then find measure of the smallest angle of parallelogram?
1) 70°
2) 110°
3) 60°
4) 1200​

Answer 1

As We know that Angles of two consecutive angles of a parallelogram are 180° .

So, We've that:-

• (3x + 10°) and (4x + 30)°

$\\ \circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\sf{ (3x + 10)^{ \circ } + (4x + 30)^{ \circ } = 180 ^{ \circ } }} \\ \\ \\ \colon\implies{\sf{ 3x + 10^{ \circ } + 4x + 30^{ \circ } = 180 ^{ \circ } }} \\ \\ \\ \colon\implies{\sf{ 7x + 40^{ \circ } = 180 ^{ \circ } }} \\ \\ \\ \colon\implies{\sf{ 7x = 180 ^{ \circ } - 40^{ \circ } }} \\ \\ \\ \colon\implies{\sf{ 7x = 140^{ \circ } }} \\ \\ \\ \colon\implies{\sf{ x = \cancel{ \dfrac{140^{ \circ } }{7} } }} \\ \\ \\ \colon\implies{\underline{\boxed{\sf{ x = 20 ^{ \circ } }}}}$

Hence,

• (3x + 10)° = (3×20+10)° = 70°
• (4x + 30)° = (4×20+30)° = 110°

${\pmb{\underline{\sf{ The \ smallest \ angle \ measure \ of \ the \ Paralellogram \ is \ 70^{ \circ } . }}}}$