Question

Help!! The angle measurements in the diagram are represented by the following expressions.

∠
A
=
5
x
+
3
4
∘
∠A=5x+34
∘
start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 5, x, plus, 34, degrees, end color #11accd
∠
B
=
2
x
+
7
6
∘
∠B=2x+76
∘

Answer 1

`\boxed{\bf \angle A=84^o}`

Explanation:

From the given diagram, we can see that ∠B & ∠C are corresponding angles, which means that they are equal. The two angles that form a straight line are supplementary angles (the sum of two supplementary angles is 180°).

`\bf 5x+34^o+\angle C=180^o`

`\bf 5x+34^o+\angle B=180^o`

`\bf 5x+34^o+2x+76^o=180^o`

Now, let's solve for x :-

`\bf (5x+34^o)+(2x+76^o)=180^o`

`\bf (5x+2x)+(34+76)=180^o`

`\bf 7x+110=180^o`

`\bf (7x+110)-110^o=180-110^o`

`\bf 7x=70^o`

`\bf \cfrac{7x}{7} =\cfrac{70}{7}`

`\boxed{\bf x=10^o}`

Now, in order to find ∠A will substitute the value of x into the expression:-
`\bf \angle A=5x+34^o`

`\bf \angle A=5(10)+34^o`

`\bf \angle A=84^o`

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