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dem82 [27]
3 years ago
11

A parallelogram has one angle that measures 118°. What are the measures of the other three angles in the parallelogram?

Mathematics
1 answer:
MariettaO [177]3 years ago
3 0

Step-by-step explanation:

<em>Given</em>

<em>We </em><em>know </em><em>that </em><em>in </em><em>a </em><em>parallelogram </em><em>opposite </em><em>angles </em><em>are </em><em>equal</em><em>. </em><em>So </em>

<em>1st </em><em>and </em><em>3rd </em><em>angles </em><em>=</em><em> </em><em>1</em><em>1</em><em>8</em><em>°</em>

<em>Let </em><em>2nd </em><em>and </em><em>4th </em><em>angles </em><em>=</em><em> </em><em>x</em>

<em>Now</em>

<em>1</em><em>1</em><em>8</em><em>°</em><em> </em><em>+</em><em> </em><em>1</em><em>1</em><em>8</em><em>°</em><em> </em><em>+</em><em> </em><em>x </em><em>+</em><em> </em><em>x </em><em>=</em><em> </em><em>3</em><em>6</em><em>0</em><em>°</em><em> </em><em>(</em><em> </em><em>Being </em><em>sum </em><em>of </em><em>angles </em><em>of </em><em>parallelogram</em><em>) </em>

<em>2</em><em>3</em><em>6</em><em>°</em><em> </em><em>+</em><em> </em><em>2x </em><em>=</em><em> </em><em>3</em><em>6</em><em>0</em><em>°</em>

<em>2x </em><em>=</em><em> </em><em>3</em><em>6</em><em>0</em><em>°</em><em> </em><em>-</em><em> </em><em>2</em><em>3</em><em>6</em><em>°</em>

<em>2x </em><em>=</em><em> </em><em>1</em><em>2</em><em>4</em><em>°</em>

<em>Therefore </em><em>x </em><em>=</em><em> </em><em>6</em><em>2</em><em>°</em>

<em>Now </em><em>the </em><em>measure </em><em>of </em><em>other </em><em>all </em><em>angles </em>

<em>118</em><em>°</em><em> </em><em>,</em><em> </em><em>6</em><em>2</em><em>°</em><em> </em><em>,</em><em> </em><em>1</em><em>1</em><em>8</em><em>°</em><em>,</em><em> </em><em>6</em><em>2</em><em>°</em>

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