Hi, please help me, i really need it thanks

Question

asked Oct 11, 2023 207k views

1 Answer

Maxbachmann · Answer 1 · 2023-10-15T20:41:07+0000

Exterior Angle Inequality Theorem

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Direction:

Use the Exterior Angle Inequality Theorem to find the measure of each angle below.

Answer:

$\huge \underline{\boxed{\sf \red{ \angle C = 27^(\circ) }}}$

$\huge \underline{\boxed{\sf \red{ \angle D = 153^(\circ) }}}$

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

$\large\tt{{180}^(\circ) = \angle A + \angle B + \angle C}$

$\large\tt{{180}^(\circ) = {35}^(\circ) + {118}^(\circ) + \angle C }$

$\large\tt{{180}^(\circ) = {153}^(\circ) + \angle C }$

$\large\tt{{180}^(\circ) - {153}^(\circ) = \angle C }$

$\large\tt{{27}^(\circ) = \angle C }$

$\large{\boxed{\tt{\angle C = {27}^(\circ)}} }$

Finding ∠D or ∠ACD

$\large\tt{ \angle A + \angle B = \angle ACD }$

$\large\tt{ {35}^(\circ) + {118}^(\circ) = \angle ACD }$

$\large\tt{ {153}^(\circ) = \angle ACD }$

$\large{\boxed{\tt{\angle ACD = {153}^(\circ) }}}$

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