I'm a bit stuck on this question, can someone help me please? Thanks if you do!

Question

asked Sep 14, 2024 130k views

1 Answer

VoidVolker · Answer 1 · 2024-09-18T03:39:27+0000

We have given that, The sum of interior angles formed by the sides of a of pentagon is 540°.

★ According To The Question:-

$\sf \longrightarrow \: Sum \: of \: all \: angles = 540 \\$

$\sf \longrightarrow \: \angle A + \angle B + \angle C + \angle D +\angle E \: = 540 \\$

$\sf \longrightarrow \: (130) + (x - 5) + (x + 30) +75 +(x - 35) \: = 540 \\$

$\sf \longrightarrow \: 130 + x - 5 + x + 30 +75 +x - 35 \: = 540 \\$

$\sf \longrightarrow \: 130 - 5+ 30+75 - 35+x + x +x \: = 540 \\$

$\sf \longrightarrow \: 130 - 5+ 30+75 - 35+3x \: = 540 \\$

$\sf \longrightarrow \: 125+ 30+75 - 35+3x \: = 540 \\$

$\sf \longrightarrow \: 155+75 - 35+3x \: = 540 \\$

$\sf \longrightarrow \: 230 - 35+3x \: = 540 \\$

$\sf \longrightarrow \: 195+3x \: = 540 \\$

$\sf \longrightarrow \: 3x \: = 540 - 195\\$

$\sf \longrightarrow \: 3x \: = 345\\$

$\sf \longrightarrow \: x \: = ( 345)/(3)\\$

$\sf \longrightarrow \: x \: = 115 \degree\\$

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★ Angle B :-

→ x - 5 °

→ 115 - 5

→ 110°

Therefore Measure of angle B is 110°