Question

The measures of all the angles in the given figure is

• A. ${35}^0,{45}^0,{115}^0,{105}^0$
• B. ${45}^0,{55}^0,{125}^0,{100}^0$
• C. ${40}^0,{50}^0,{120}^0,{105}^0$
• D. ${25}^0,{65}^0,{135}^0,{95}^0$

Answer 1

The correct option is B

${45}^0,{55}^0,{125}^0,{100}^0$

Inner angle at C is $={180}^0-{135}^0={45}^0$ [Linear pair]

Inner angle at B = ${180}^0-({80}^0+{45}^0)={180}^0-{125}^0$ [Sum of all the angles of a triangle is ${180}^0$]

$={55}^0$

Outer angle at B is $={180}^0-{55}^0={125}^0$ [Linear pair]

Outer angle at A is $={360}^0-({125}^0+{135}^0)={360}^0-{260}^0$ [Sum of all the exterior angles of triangle is ${360}^0$]

$={100}^0$