In the figure, ray MO bisects ZLMN, MLLMO = (13z- 31)°, andMZNMO = (x + 53)°. Find the following.%3Dm/LMO =%3Dm/LMN =%3D

We have to find value of x, m<LMO and m<LMN where, m<LMO=13x-31°m<NMO=x+53° Given figure…

Answered: In the figure, ray MO bisects ZLMN,…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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In the figure, ray MO bisects ZLMN, MLLMO = (13z- 31)°, and
MZNMO = (x + 53)°. Find the following.
%3D
m/LMO =
%3D
m/LMN =
%3D

Expert Solution

Step 1

We have to find value of $x, m < L M O$ and $m < L M N$ where,

$\begin{array}{rcl} m & < & L M O = (13 x - 31) ° \\ m & < & N M O = (x + 53) ° \end{array}$

Given figure is:

Here, $M O$ is bisecting the angle $< L M N$

therefore,

$< L M O = < N M O$

Putting values,

$\begin{array}{rcl} < & L M O = < N M O \\ (13 x - 31) ° & = & (x + 53) ° \\ 13 x - 31 & = & x + 53 \\ 13 x - x & = & 53 + 31 \\ 12 x & = & 84 \\ x & = & \frac{84}{12} \\ = & 7 \end{array}$

Hence, value of $x$ is $7$ .

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In the figure, ray MO bisects ZLMN, MLLMO = (13z- 31)°, and MZNMO = (x + 53)°. Find the following. %3D m/LMO = %3D m/LMN = %3D