Exterior Angle Inequality Theorem
[tex] \normalsize\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]
Direction:
Use the Exterior Angle Inequality Theorem to find the measure of each angle below.
Answer:
[tex] \huge \underline{\boxed{\sf \red{ \angle C = 27^{\circ} }}}[/tex]
[tex] \huge \underline{\boxed{\sf \red{ \angle D = 153^{\circ} }}}[/tex]
Solution:
Add the ∠A and ∠B and minus it to 180° to know the measure of ∠C. To find the ∠D add only the ∠A and ∠B.
Finding ∠C
- [tex]\large\tt{{180}^{\circ} = \angle A + \angle B + \angle C}[/tex]
- [tex]\large\tt{{180}^{\circ} = {35}^{\circ} + {118}^{\circ} + \angle C }[/tex]
- [tex]\large\tt{{180}^{\circ} = {153}^{\circ} + \angle C }[/tex]
- [tex]\large\tt{{180}^{\circ} - {153}^{\circ} = \angle C }[/tex]
- [tex]\large\tt{{27}^{\circ} = \angle C }[/tex]
- [tex]\large{\boxed{\tt{\angle C = {27}^{\circ}}} }[/tex]
Finding ∠D or ∠ACD
- [tex]\large\tt{ \angle A + \angle B = \angle ACD }[/tex]
- [tex]\large\tt{ {35}^{\circ} + {118}^{\circ} = \angle ACD }[/tex]
- [tex]\large\tt{ {153}^{\circ} = \angle ACD }[/tex]
- [tex]\large{\boxed{\tt{\angle ACD = {153}^{\circ} }}}[/tex]
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To understand easily, just tap the attachment given.
[tex] \normalsize\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]
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