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In the figure, find p || q. Find m angle 1

In the figure, find p || q. Find m angle 1-example-1
User Tvieira
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1 Answer

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The value of m∠1 = 68°

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

In the triangle SAB

m∠ASB+m∠SAB+m∠SBA = 180°

Find the measure of angle ASB

we know that

m∠ASB + 115° = 180° ----> by supplementary angles (form a linear pair)

m∠ASB = 180° - 115° = 65°

Find the measure of angle SBA

we know that

m∠SBC = 133º ----> by corresponding angles

Remember that

m∠SBA+m∠SBC = 180° ---> by supplementary angles (form a linear pair)

substitute

m∠SBA+133° = 180°

m∠SBA 180°-133° = 47°

Find the measure of angle SAB

m∠ASB+m∠SAB+m/SBA = 180°

substitute

65°+m∠SAB +47° = 180°

m∠SAB 180° - 112° = 68°

Find the measure of angle 1

we know that m1 = m/SAB ----> by vertical angles

therefore

m∠1 = 68°

User Mitun
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