Question

(8)
triangle ABC congruent EDF, if angleE = 40°, angleF = 110° then angleB is​

Answer 1

Answer:

30°

Step-by-step explanation:

in triangle EDF

angle E= 40°

angle F= 110°

angle D= 180-(110+40)

= 180-150

= 30°

since, triangle ABC is congruent to EDF

then angle B is equal to angle D

angle B= 30°

Answer 2

Answer:

$\large{\underline{\underline{\textsf{\maltese{\red{Right Question }}}}}}$

♣ Triangle ∠ABC congruent ∠EDF, if angle ∠E = 40°, angle ∠F = 110° then angle ∠D is?

$\rule{300}{3}$

$\large{\underline{\underline{\textsf{\maltese{\red{Given}}}}}}$

• ♣ Triangle ABC congruent EDF
• ♣ Angle E = 40°, Angle F = 110°

$\large{\underline{\underline{\textsf{\maltese{\red{To Find }}}}}}$

• ♣ Angle B

$\rule{300}{3}$

$\large{\underline{\underline{\textsf{\maltese{\red{Solution}}}}}}$

Here triangle ABC congruent to EDF

Then,

• $\clubsuit \: \sf\angle{ A }= \angle{E}$
• $\clubsuit \: \sf \angle{B}= \angle{D}$
• $\clubsuit \: \sf \angle{C}= \angle{F}$

As we know that

$: \implies\sf \angle{A }+ \angle{B} + \angle{ C }={180 \degree}$

According to the Question

$: \implies \bf \angle \: E+\angle \: D+\angle \: F=180 \degree$

• Substituting the values

${: \implies \sf \angle \: 40 \degree+\angle \:D +\angle \: 110 \degree=180 \degree}$

${: \implies \sf \angle \: 150 \degree +\angle \: D \degree=180 \degree}$

${: \implies \sf \angle \: D \degree=180 \degree - 150 \degree }$

${: \implies \bf \angle \: D \degree = 30 \degree }$

$\large \spadesuit \: \underline{ \boxed{\sf \purple{ \angle \: D \degree=30\degree }}} \: \spadesuit$

$\rule{300}{3}$

$\large{\underline{\underline{\textsf{\maltese{\red{Verification}}}}}}$

$: \implies \bf \angle \: E+\angle \: D+\angle \: F=180 \degree$

• Substituting the values

${: \implies \sf 40 \degree+30 \degree+ 110 \degree=180 \degree}$

${: \implies \sf 180 \degree=180 \degree}$

$\large \spadesuit \: \underline{ \boxed{\sf \purple{LHS=RHS}}} \: \spadesuit \\ \: \: \: \: \sf \underline{Hence \: Verified} \: \checkmark$

$\rule{300}{3}$

$\large{\underline{\underline{\textsf{\maltese{\red{Therefore}}}}}}$

• ♣ Angle D is 40⁰.