Question

Determine a medida dos ângulos indicados

Answer 1

a)

$\mathsf{x+105^{\circ}+98^{\circ}+87^{\circ}=360^{\circ}}\\\mathsf{x+290^{\circ}=360^{\circ}}\\\mathsf{x=360^{\circ}-290^{\circ}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=70^{\circ}}}}}}$

b)

$\mathsf{x+80^{\circ}+82^{\circ}=180^{\circ}}\\\mathsf{x+162^{\circ}=180^{\circ}}\\\mathsf{x=180^{\circ}-162^{\circ}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=18^{\circ}}}}}}\\\mathsf{x+90^{\circ}+y+90^{\circ}=360^{\circ}}\\\mathsf{y+180^{\circ}+18^{\circ}=360^{\circ}}\\\mathsf{y=360^{\circ}-198^{\circ}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{y=162^{\circ}}}}}}$

c)

$\mathsf{a+\dfrac{a}{2}+2a+\dfrac{3a}{2}=360^{\circ}\cdot2}\\\mathsf{2a+a+4a+3a=720^{\circ}}\\\mathsf{10a=720^{\circ}}\\\mathsf{a=\dfrac{720^{\circ}}{10}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{a=72^{\circ}}}}}}\\\mathsf{a+b+90^{\circ}=180^{\circ}}\\\mathsf{72^{\circ}+b+90^{\circ}=180^{\circ}}\\\mathsf{b=180^{\circ}-162^{\circ}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{b=18^{\circ}}}}}}$