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Vladimir [108]
4 years ago
14

If two angles form a linear pair and then m<1=2x+20 and m<2=48x find the measure of each angle

Mathematics
2 answers:
Virty [35]4 years ago
7 0
Angle 1= 26.4
Angle 2= 153.6
Liono4ka [1.6K]4 years ago
3 0

Answer:

Linear pair states that it is the pair of adjacent angle formed when two lines intersect.

If two angles form a linear pair then their sum add up to 180 degree.

Given that:

m\angle 1 = 2x+20 and m\angle 2 = 48x are two angles form a linear pair.

Then by definition of linear pair;

m\angle 1+m\angle 2 = 180^{\circ}

Substitute the given values and solve for x;

2x+20+48x = 180^{\circ}

Combine like terms;

50x+20= 180^{\circ}

Subtract 20 from both sides we get;

50x= 160^{\circ}

Divide both sides by 50 we get;

x = 3.2

Then; the measure of these angles are;

m\angle 1 = 2(3.2)+20 = 6.4+20 =26.4^{\circ}

m\angle 2 = 48(3.2)= 153.6^{\circ}

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Given: m∠ADB = m∠CDB<br><br> AD ≅ DC <br> Prove: m∠BAC = m∠BCA <br> BD⊥ AC
puteri [66]

Answer:

The proof is explained below.

Step-by-step explanation:

Given m∠ADB = m∠CDB and AD ≅ DC

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In ΔADO and ΔCDO

∠OAD=∠OCD          (∵ADC is an isosceles triangle)

AD=DC                     (∵Given)

∠ADO=∠CDO          (∵Given)

By ASA rule, ΔADO≅ΔCDO

In ΔBAD and ΔBCD

AD=DC                (∵ABC is an isosceles triangle)

∠ADB=∠CDB      (∵Given)

DB=DB                (∵common)

By ASA rule, ΔADB≅ΔCDB

Now, ΔADB≅ΔCDB and  ΔADO≅ΔCDO

⇒  ΔADB-ΔADO≅ΔCDB-ΔCDO

⇒  ΔABO≅ΔCBO

Hence, by CPCT,  m∠BAC = m∠BCA

Now, we have to prove that BD⊥ AC i.e we have to prove m∠BOA=90°

Now, ΔABO≅ΔCBO therefore by CPCT,  m∠BOA = m∠BOC

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⇒  m∠BOA + m∠BOA=180°

⇒  2m∠BOA=180°  ⇒  m∠BOA=90°

Hence,  BD⊥ AC

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4 years ago
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Note that the bases (top horizontal line segment and the bottom horizontal line segment) are <em>parallel</em> while the sides are congruent.

~

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