Question

Use the information given in the following figure to find X. С (ii) ZB and C. 3x - 5° D (8x 15° 2x + 40 B A​

Answer 1

Given :

• ∠A = Perpendicular = 90°
• ∠B = 2x + 4°
• ∠C = 3x - 5°
• ∠D = 8x - 15°

To find :

1. x
2. ∠B and ∠C

Solution :

We know that,

The sum of the measures of angles of quadrilateral is 360°

As, according to the question,

$\displaystyle\implies{ \rm \angle A + \angle B + \angle C + \angle D = 360 \degree} \\ \implies { \rm90 \degree + (2x + 4 ) \degree+ (3x - 5 )\degree+ (8x - 15 )\degree= 360 \degree} \\ \implies{ \rm90 + 2x + 4 \: + 3x - 5 + 8x - 15 = 360 \degree} \\ \implies { \rm13x + 74 \degree = 360 \degree} \\ \implies { \rm13x = 360 - 74} \\ \implies{ \rm 13x = 286 \degree} \\ \implies { \rm \: x = \frac{286}{13} } \\ \implies \boxed { \red {x = 22 \degree}}$

Measure of ∠B = 2x + 4

= 2(22) + 4

= 44 + 4

= 48°

Measure of ∠C = 3x - 5°

= 3(22) - 5

= 66 - 5

= 61°

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