Use drawings, as needed, to answer each question. ℓ[m, with transversal t, and OQ bisects ∠M O

step 1 So given this information that line L and M are parallel to each other and we have a transversal

Use drawings, as needed, to answer each question. ℓ[m, with...

Use drawings, as needed, to answer each question. $\boldsymbol{\ell}[m, \text { with transversal } t,$ and $\overrightarrow{\mathrm{OQ}}$ bisects $\angle M O N$ If $\mathrm{m} \angle \mathrm{I}=112^{\circ},$ find the following: a) $m \angle 2$ b) $m \angle 4$ c) $m \angle 5$ d) $\mathrm{m} \angle \mathrm{MOQ}$ (GRAPH CAN'T COPY)

Use drawings, as needed, to answer each question.
$\boldsymbol{\ell}[m, \text { with transversal } t,$ and $\overrightarrow{\mathrm{OQ}}$ bisects $\angle M O N$
If $\mathrm{m} \angle \mathrm{I}=112^{\circ},$ find the
following:
a) $m \angle 2$
b) $m \angle 4$
c) $m \angle 5$
d) $\mathrm{m} \angle \mathrm{MOQ}$
(GRAPH CAN'T COPY)

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Key Concepts

Parallel Lines and Transversals

When two parallel lines are intersected by a transversal, several predictable angle relationships occur. This includes corresponding angles, alternate interior angles, and alternate exterior angles being congruent, while same-side interior angles are supplementary. Understanding these relationships is essential for solving problems involving angle measures in geometric figures.

Vertical Angles

Vertical angles are the pairs of opposite angles formed by the intersection of two lines. They are always congruent. Recognizing vertical angles helps in determining unknown angle measures in various geometric configurations.

Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. This concept applies especially to linear pairs, where two adjacent angles form a straight line. It is a key idea for solving problems where the sum of adjacent angles is involved.

Angle Bisector

An angle bisector is a ray or segment that divides an angle into two congruent angles. Using an angle bisector in geometric problems helps to create symmetry and determine equal parts within an angle, which is essential for calculating unknown measures.

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